Home
Class 12
MATHS
Integrate the rational functions(x^3+x+...

Integrate the rational functions`(x^3+x+1)/(x^2-1)`

Text Solution

AI Generated Solution

To solve the integral \(\int \frac{x^3 + x + 1}{x^2 - 1} \, dx\), we will perform polynomial long division and then integrate the resulting expression. ### Step 1: Polynomial Long Division We start by dividing \(x^3 + x + 1\) by \(x^2 - 1\). 1. Divide the leading term: \(\frac{x^3}{x^2} = x\). 2. Multiply \(x\) by \(x^2 - 1\): \(x(x^2 - 1) = x^3 - x\). 3. Subtract this from \(x^3 + x + 1\): ...
Promotional Banner

Topper's Solved these Questions

  • INTEGRALS

    NCERT|Exercise MISCELLANEOUS EXERCISE|44 Videos

  • INTEGRALS

    NCERT|Exercise EXERCISE 7.3|24 Videos

  • INTEGRALS

    NCERT|Exercise EXERCISE 7.7|14 Videos

  • DIFFERENTIAL EQUATIONS

    NCERT|Exercise EXERCISE 9.1|12 Videos

  • INVERSE TRIGONOMETRIC FUNCTIONS

    NCERT|Exercise MISCELLANEOUS EXERCISE|17 Videos

Similar Questions

Explore conceptually related problems

Integrate the rational functions (2x-3)/((x^(2)-1)(2x-4))

Integrate the rational functions (3x-1)/((x+2)^(2))

Integrate the rational functions (3x-1)/((x-1)(x-2)(x-3))

Integrate the rational functions (x)/((x^(2)+1)(x-1))

Integrate the rational functions x/((x+1)(x+2)

Integrate the rational functions (1)/(x^(2)-9)

Integrate the rational functions (1)/(x^(4)-1)

Integrate the rational functions (1)/(x(x^(4)-1))

Integrate the rational functions (5x)/((x+1)(x^(2)-4))

Integrate the rational functions (x^(2)+1)(x^(2)+2)(x^(2)+3)(x^(2)+4)