Home
Class 12
MATHS
int(x^(3)-1)/(x^(3)+x) dx is equal to:...

`int(x^(3)-1)/(x^(3)+x)` dx is equal to:

A

`x-log_(e)|x|+log_(e)(x^(2)+1)-tan^(-1)x+C`

B

`x-log_(e)|x|+(1)/(2)log_(e)(x^(2)+1)-tan^(-1)x+C`

C

`x+log_(e)|x|+(1)/(2)log_(e)(x^(2)+1)+tan^(-1)x+C`

D

none of these

Text Solution

Verified by Experts

The correct Answer is:
B
`int(x^(3)-1)/(x^(3)+x)dx=int(1+(1)/(1+x^(2))-(1)/(x)+(x)/(x^(2)+1))dx`
`=x-tan^(-1)x-log_(e)|x|+(1)/(2)log_(e)(x^(2)+1)+C`
Promotional Banner

Topper's Solved these Questions

  • INDEFINITE INTEGRATION

    CENGAGE|Exercise Subjective Type|6 Videos

  • INDEFINITE INTEGRATION

    CENGAGE|Exercise Comprehension Type|2 Videos

  • INDEFINITE INTEGRATION

    CENGAGE|Exercise JEE Advanced Previous Year|1 Videos

  • HYPERBOLA

    CENGAGE|Exercise JEE Advanced Previous Year|14 Videos

  • INEQUALITIES AND MODULUS

    CENGAGE|Exercise Single correct Answer|21 Videos

Similar Questions

Explore conceptually related problems

int(2x^(3)-1)/(x^(4)+x)dx is equal to

int(x^(3)-1)^(1//3)x^(5)dx is equal to

I=int((x+a)^(3))/(x^(3))dx is equal to

int(x^(3)-x)/(1+x^(6))dx is equal to

int x^(3) dx is equal to :

If int(x^(5))/(sqrt(1+x^(3)))dx is equal to

int(x^(3)dx)/(x^(2)+1)^(3) is equal to

int x^(1/3)(2+x^(2/3))dx" is equal to

int(x+1)/(2x^((3)/(2)))dx is equal to

int(x-3)/((x-1)^(3)).e^(x)dx is equal to