Home
Class 12
MATHS
Evaluate: int(x^2)/((x^2+1)(x^2+4))\ dx...

Evaluate: `int(x^2)/((x^2+1)(x^2+4))\ dx`

Text Solution

Verified by Experts

`int frac{x^{2}}{(x^{2}+1)(x^{2}+4)} d x`

`=int frac{4 x^{2}}{(4 x^{2}+4)(x^{2}+4)} d x`

`=4 int frac{x^{2}}{(4 x^{2}+4)(x^{2}+4)} d x`

`=frac{4}{3} int frac{(4 x^{2}+4)-(x^{2}+4)}{(4 x^{2}+4)(x^{2}+4)} d x`

`=frac{4}{3} int frac{(4 x^{2}+4) d x}{(4 x^{2}+4)(x^{2}+4)}-frac{4}{3} int frac{(x^{2}+4) d x}{(4 x^{2}+4)(x^{2}+4)}`

`=frac{4}{3} int frac{{dx}}{({x}^{2}+4)}-frac{4}{3} int frac{{dx}}{(4 {x}^{2}+4)}`

`=frac{4}{3} int frac{d x}{x^{2}+4}-frac{4}{12} int frac{d x}{x^{2}+1}`

`=frac{4}{3} times frac{1}{2} tan ^{-1} frac{x}{2}-frac{1}{3} tan ^{-1} x+c`

...
Promotional Banner

Topper's Solved these Questions

  • INCREASING AND DECREASING FUNCTION

    RD SHARMA|Exercise Solved Examples And Exercises|232 Videos

  • INVERSE TRIGONOMETRIC FUNCTION

    RD SHARMA|Exercise Solved Examples And Exercises|523 Videos

Similar Questions

Explore conceptually related problems

Evaluate: int(x^2+1)/((x^2+4)(x^2+25))\ dx

Evaluate: int(5x)/((x+1)(x^2-4))\ dx

Evaluate: int(x^2)/((x-1)(x+1)^2)\ dx

Evaluate: int(x)/((x-1)(x^(2)+4))dx

Evaluate: int(1)/((x^(2)+1)(x^(2)+4))dx

Evaluate: int(2x^(2)+1)/(x^(2)(x^(2)+4))dx

Evaluate: int(x^(2))/((x^(2)+1)(3x^(2)+4))dx

Evaluate : int (dx)/((2x+1)(x^(2)+4))

Evaluate int (3x^2+4x-5)/((x^2-1)(x+2))dx

Evaluate: int(x^2)/(x^4+x^2-2)\ dx