Home
Class 12
MATHS
int (1+2x^(6))/((1-x^(6))^(3//2))dx is e...

`int (1+2x^(6))/((1-x^(6))^(3//2))dx` is equal to

A

`(2x)/(sqrt(1+x^(6)))+c`

B

`(1)/(sqrt((1)/(x^(2))-x^(4)))+c`

C

`(x)/(sqrt((1)/(x^(2))-x^(4)))+c`

D

`(x^(2)+x)/(sqrt(1-x^(6)))+C`

Text Solution

Verified by Experts

The correct Answer is:
B
`I=int (1+2x^(6))/((1-x^(6))^(3//2))dx=int((1)/(x^(3))+2x^(3))/((1)/(x^(2))-x^(4))^((3)/(2))dx`
put `(1)/(x^(2))-x^(4)=t`
` :. ((-2)/(x^(3))-4x^(3))dx=dt`
or `((1)/(x^(3))+2x^(3))dx= -(dt)/(2)`
` :. I= -(1)/(2)int (dt)/(t^((3)/(2)))`
`= -(1)/(2)(t^(-1//2))/(2-1//2)+c`
` =(1)/(sqrt(t))+c`
`=(1)/(sqrt((1)/(x^(2))-x^(4)))+c`
Promotional Banner

Topper's Solved these Questions

  • INDEFINITE INTEGRATION

    CENGAGE|Exercise Exercise (Multiple)|17 Videos

  • INDEFINITE INTEGRATION

    CENGAGE|Exercise Exercise (Comprehension)|17 Videos

  • INDEFINITE INTEGRATION

    CENGAGE|Exercise Exercise 7.9|15 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_(1)^(2)x^(2)dx is equal to

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

int_(1)^(2)(dx)/(x^(2)) is equal to

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

The integral int(2x^(3)-1)/(x^(4)+x)dx is equal to (here C is a constant of intergration)

int e^(sin^(-1)x)((log_(e)x)/(sqrt(1-x^(2)))+(1)/(x))dx is equal to

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

int(x^9)/((4x^2+1)^6) dx is equal to

int sqrt(x)(1+x^(1//3))^(4)dx " is equal to "

int_(5/2)^5(sqrt((25-x^2)^3))/(x^4)dx is equal to (a) pi/6 (b) (2pi)/3 (c) (5pi)/6 (d) pi/3