Home
Class 12
MATHS
Integrate the rational functions(3x+5)/...

Integrate the rational functions`(3x+5)/(x^3-x^2-x+1)`

Text Solution

AI Generated Solution

To solve the integral of the rational function \(\frac{3x + 5}{x^3 - x^2 - x + 1}\), we will follow these steps: ### Step 1: Factor the Denominator First, we need to factor the denominator \(x^3 - x^2 - x + 1\). We can group the terms: \[ x^3 - x^2 - x + 1 = x^2(x - 1) - 1(x - 1) = (x^2 - 1)(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 (1)/(x^(2)-9)

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

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

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

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

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

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

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

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

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