Home
Class 12
MATHS
Integrate the rational functions2/((1-x...

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

Text Solution

Verified by Experts

Let` 2/[(1−x)(1+x^2)]​=A/(1−x)​+(Bx+C)/(1+x^2)`
⇒`2=A(1+x^2)+(Bx+C)(1−x)`
⇒`2=A+Ax^2+Bx−Bx^2+C+Cx`
Equating the coefficient of `x^2,x`, and constant term, we obtain
`A−B=0`
`B−C=0`
`A+C=2`
On solving these questions, we obtain
...
Promotional Banner

Topper's Solved these Questions

  • INTEGRALS

    NCERT ENGLISH|Exercise MISCELLANEOUS EXERCISE|44 Videos

  • INTEGRALS

    NCERT ENGLISH|Exercise EXERCISE 7.3|24 Videos

  • INTEGRALS

    NCERT ENGLISH|Exercise Exercise 7.11|20 Videos

  • DIFFERENTIAL EQUATIONS

    NCERT ENGLISH|Exercise EXERCISE 9.1|12 Videos

  • INVERSE TRIGONOMETRIC FUNCTIONS

    NCERT ENGLISH|Exercise Solved Examples|13 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 x/((x+1)(x+2)

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

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

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

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

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)