Data Modelling & AI Data Structure & Algorithm

Program to find the indefinite Integration of the given Polynomial

23 June 2025

0

Given a polynomial string str, the task is to integrate the given string and print the string after integrating it. Note: The input format is such that there is a whitespace between a term and the ‘+’ symbol. Examples:

Input: str = “4X³ + 3X¹ + 2X²” Output: X⁴ + (3/2)X² + (2/3)X³ + C Input: str = “5X³ + 7X¹ + 2X² + 1X⁰” Output: (5/4)X⁴ + (7/2)X² + (2/3)X³ + X^q + C

Approach: The idea is to observe that when the given equation consists of multiple polynomials $p(x) = p1(x) + p2(x)$ , the integration of the given polynomial $P(x) = P1(x) + P2(x)$ . Also it is known that the indefinite integral of $p(x) = AX^N$ is $P(x) = \frac{A*X^{N + 1}}{N + 1 }+ C$ . Therefore, we split the given string and integrate every term in it. Below is the implementation of the above approach:

CPP

// C++ program to find the indefinite
// integral of the given polynomial
   
#include "bits/stdc++.h"
#define MOD (1e9 + 7);
using ll = int64_t;
using ull = uint64_t;
#define ll long long
using namespace std;
   
// Function to perform the integral
// of each term
string inteTerm(string pTerm)
{
    // Get the coefficient
    string coeffStr = "", S = "";
    int i;
   
    // Loop to iterate and get the
    // Coefficient
    for (i = 0; pTerm[i] != 'x'; i++)
        coeffStr.push_back(pTerm[i]);
    long long coeff
        = atol(coeffStr.c_str());
   
    string powStr = "";
   
    // Loop to find the power
    // of the term
    for (i = i + 2; i != pTerm.size(); i++)
        powStr.push_back(pTerm[i]);
   
    long long power
        = atol(powStr.c_str());
    string a, b;
    ostringstream str1, str2;
   
    // For ax^n, we find a*x^(n+1)/(n+1)
    str1 << coeff;
    a = str1.str();
    power++;
    str2 << power;
    b = str2.str();
    S += "(" + a + "/" + b + ")X^" + b;
   
    return S;
}
   
// Function to find the indefinite
// integral of the given polynomial
string integrationVal(string& poly)
{
   
    // We use istringstream to get the
    // input in tokens
    istringstream is(poly);
   
    string pTerm, S = "";
   
    // Loop to iterate through
    // every term
    while (is >> pTerm) {
   
        // If the token = '+' then
        // continue with the string
        if (pTerm == "+") {
            S += " + ";
            continue;
        }
   
        if (pTerm == "-") {
            S += " - ";
            continue;
        }
   
        // Otherwise find
        // the integration of
        // that particular term
        else
            S += inteTerm(pTerm);
    }
    return S;
}
   
// Driver code
int main()
{
    string str
        = "5x^3 + 7x^1 + 2x^2 + 1x^0";
    cout << integrationVal(str)
         << " + C ";
    return 0;
}

Java

// Java program to find the indefinite
// integral of the given polynomial
import java.util.*;
 
class GFG {
 
  // Function to perform the integral
  // of each term
  static String inteTerm(String pTerm)
  {
    // Get the coefficient
    String coeffStr = "", S = "";
    int i;
 
    // Loop to iterate and get the
    // Coefficient
    for (i = 0; pTerm.charAt(i) != 'x'; i++)
      coeffStr += (pTerm.charAt(i));
    long coeff = Long.valueOf(coeffStr);
 
    String powStr = "";
 
    // Loop to find the power
    // of the term
    for (i = i + 2; i != pTerm.length(); i++)
      powStr += (pTerm.charAt(i));
 
    long power = Long.valueOf(powStr);
    String a, b;
 
    // For ax^n, we find a*x^(n+1)/(n+1)
    a = String.valueOf(coeff);
    power++;
    b = String.valueOf(power);
    S += "(" + String.valueOf(a) + "/"
      + String.valueOf(b) + ")X^"
      + String.valueOf(b);
 
    return S;
  }
 
  // Function to find the indefinite
  // integral of the given polynomial
  static String integrationVal(String poly)
  {
 
    // We use iStringstream to get the
    // input in tokens
    String[] is1 = poly.split(" ");
 
    String S = "";
 
    // Loop to iterate through
    // every term
    for (String pTerm : is1) {
 
      // If the token = '+' then
      // continue with the String
      if (pTerm.equals("+")) {
        S += " + ";
        continue;
      }
 
      if (pTerm.equals("-")) {
        S += " - ";
        continue;
      }
 
      // Otherwise find
      // the integration of
      // that particular term
      else
        S += inteTerm(pTerm);
    }
    return S;
  }
 
  // Driver code
  public static void main(String[] args)
  {
    String str = "5x^3 + 7x^1 + 2x^2 + 1x^0";
    System.out.println(integrationVal(str) + " + C ");
  }
}
 
// This code is contributed by phasing17

Python3

# Python3 program to find the indefinite
# integral of the given polynomial
MOD = 1000000007
 
# Function to perform the integral
# of each term
def inteTerm( pTerm):
 
    # Get the coefficient
    coeffStr = ""
    S = "";
   
    # Loop to iterate and get the
    # Coefficient
    i = 0
    while pTerm[i] != 'x':
        coeffStr += (pTerm[i]);
        i += 1
    coeff = int(coeffStr)
   
    powStr = "";
   
    # Loop to find the power
    # of the term
    for j in range(i + 2, len(pTerm)):
        powStr += (pTerm[j]);
   
    power = int(powStr)
    a = ""
    b = "";
   
    # For ax^n, we find a*x^(n+1)/(n+1)
    str1 = coeff;
    a = str1
    power += 1
    str2 = power;
    b = str2
    S += "(" + str(a) + "/" + str(b) + ")X^" + str(b);
   
    return S;
 
   
# Function to find the indefinite
# integral of the given polynomial
def integrationVal(poly):
 
    # We use istringstream to get the
    # input in tokens
    is1 = poly.split();
   
    S = "";
   
    # Loop to iterate through
    # every term
    for pTerm in is1:
     
        # If the token = '+' then
        # continue with the string
        if (pTerm == "+") :
            S += " + ";
            continue;
         
   
        if (pTerm == "-"):
            S += " - ";
            continue;
         
   
        # Otherwise find
        # the integration of
        # that particular term
        else:
            S += inteTerm(pTerm);
     
    return S;
 
   
# Driver code
str1 = "5x^3 + 7x^1 + 2x^2 + 1x^0";
print(integrationVal(str1) + " + C ");
 
 
# This code is contributed by phasing17

C#

// C# program to find the indefinite
// integral of the given polynomial
 
using System;
using System.Collections.Generic;
 
class GFG {
 
    // Function to perform the integral
    // of each term
    static string inteTerm(string pTerm)
    {
        // Get the coefficient
        string coeffStr = "", S = "";
        int i;
 
        // Loop to iterate and get the
        // Coefficient
        for (i = 0; pTerm[i] != 'x'; i++)
            coeffStr += (pTerm[i]);
        long coeff = Convert.ToInt64(coeffStr);
 
        string powStr = "";
 
        // Loop to find the power
        // of the term
        for (i = i + 2; i != pTerm.Length; i++)
            powStr += (pTerm[i]);
 
        long power = Convert.ToInt64(powStr);
        string a, b;
 
        // For ax^n, we find a*x^(n+1)/(n+1)
        a = Convert.ToString(coeff);
        power++;
        b = Convert.ToString(power);
        S += "(" + Convert.ToString(a) + "/"
             + Convert.ToString(b) + ")X^"
             + Convert.ToString(b);
 
        return S;
    }
 
    // Function to find the indefinite
    // integral of the given polynomial
    static string integrationVal(string poly)
    {
 
        // We use istringstream to get the
        // input in tokens
        string[] is1 = poly.Split(" ");
 
        string S = "";
 
        // Loop to iterate through
        // every term
        foreach(string pTerm in is1)
        {
 
            // If the token = '+' then
            // continue with the string
            if (pTerm == "+") {
                S += " + ";
                continue;
            }
 
            if (pTerm == "-") {
                S += " - ";
                continue;
            }
 
            // Otherwise find
            // the integration of
            // that particular term
            else
                S += inteTerm(pTerm);
        }
        return S;
    }
 
    // Driver code
    public static void Main(string[] args)
    {
        string str = "5x^3 + 7x^1 + 2x^2 + 1x^0";
        Console.WriteLine(integrationVal(str) + " + C ");
    }
}
 
// This code is contributed by phasing17

Javascript

// JavaScript program to find the indefinite
// integral of the given polynomial
   
let MOD = (1e9 + 7);
 
   
// Function to perform the integral
// of each term
function inteTerm( pTerm)
{
    // Get the coefficient
    let coeffStr = "", S = "";
    let i;
   
    // Loop to iterate and get the
    // Coefficient
    for (i = 0; pTerm[i] != 'x'; i++)
        coeffStr += (pTerm[i]);
    let coeff
        = parseInt(coeffStr)
   
    let powStr = "";
   
    // Loop to find the power
    // of the term
    for (i = i + 2; i != pTerm.length; i++)
        powStr += (pTerm[i]);
   
    let power
        = parseInt(powStr)
    let a = "", b = "";
    let str1, str2;
   
    // For ax^n, we find a*x^(n+1)/(n+1)
    str1 = coeff;
    a = str1
    power++;
    str2 = power;
    b = str2
    S += "(" + a + "/" + b + ")X^" + b;
   
    return S;
}
   
// Function to find the indefinite
// integral of the given polynomial
function integrationVal(poly)
{
   
    // We use istringstream to get the
    // input in tokens
    let is = poly.split(" ");
   
    let pTerm, S = "";
   
    // Loop to iterate through
    // every term
    for (pTerm of is)
    {
        // If the token = '+' then
        // continue with the string
        if (pTerm == "+") {
            S += " + ";
            continue;
        }
   
        if (pTerm == "-") {
            S += " - ";
            continue;
        }
   
        // Otherwise find
        // the integration of
        // that particular term
        else
            S += inteTerm(pTerm);
    }
    return S;
}
   
// Driver code
let str = "5x^3 + 7x^1 + 2x^2 + 1x^0";
console.log(integrationVal(str) + " + C ");
 
 
// This code is contributed by phasing17

Output:

(5/4)X^4 + (7/2)X^2 + (2/3)X^3 + (1/1)X^1 + C

Feeling lost in the world of random DSA topics, wasting time without progress? It’s time for a change! Join our DSA course, where we’ll guide you on an exciting journey to master DSA efficiently and on schedule.
Ready to dive in? Explore our Free Demo Content and join our DSA course, trusted by over 100,000 neveropen!

Program to find the indefinite Integration of the given Polynomial

CPP

Java

Python3

C#

Javascript

Multimodal RAG Made Simple: RAG-Anything + Milvus Instead of 20 Separate Tools

Introducing the Embedding Function: How Milvus 2.6 Streamlines Vectorization and Semantic Search

Choosing a vector database for ANN search at Reddit

LEAVE A REPLY Cancel reply

Most Popular

I’m tired of how Google Messages still can’t get this one thing right

The One UI 8.5 setting that finally fixed my Galaxy’s most annoying quirk

Leak suggests Samsung Gallery will adopt one of Google Photos’ best tricks

I stopped using Google Maps and this Android app made me love driving again

EDITOR PICKS

I’m tired of how Google Messages still can’t get this one thing right

The One UI 8.5 setting that finally fixed my Galaxy’s most annoying quirk

Leak suggests Samsung Gallery will adopt one of Google Photos’ best tricks

POPULAR POSTS

I’m tired of how Google Messages still can’t get this one thing right

The One UI 8.5 setting that finally fixed my Galaxy’s most annoying quirk

Leak suggests Samsung Gallery will adopt one of Google Photos’ best tricks

POPULAR CATEGORY

ABOUT US

FOLLOW US