Home
Class 12
MATHS
int(1)/(x(1+root(3)(x))^(2))dxis equal t...

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

A

`3{"log"((x^(1//3))/(1+x^(1//3)))+(1)/(1+root(3)(x))}+C`

B

`3{"log"((x^(1//3))/(1+x^(1//3)))+(1)/(1+x^(1//3))}+C`

C

`3{"log"((x^(1//3))/(1+x^(1//3)))-(1)/(1+x^(1//3))}+C`

D

none of these

Text Solution

Verified by Experts

The correct Answer is:
a
Let `I=int(1)/(x(1+root(3)(x))^(2))dx=int(1)/(t^(3)(1+t)^(2))3t^(2)dt`
`rArr I=3int(1)/(t(t+1)^(2))dt=3 int{(1)/(t)-(1)/(t+1)-(1)/((t+1)^(2))}dt`
`rArr I=3 { log_(e)t-log(t+1)+(1)/(t+1)}+C`
`rArrI=3 {log_(e)((t)/(t+1))+(1)/(t+1)}+C`
`rArrI=3{log_(e)(x^(1//3)/(1+x^(1//3)))+(1)/(x^(1//3)+1)}+C`.
Promotional Banner

Topper's Solved these Questions

  • INDEFINITE INTEGRALS

    OBJECTIVE RD SHARMA|Exercise Section II - Assertion Reason Type|3 Videos

  • INDEFINITE INTEGRALS

    OBJECTIVE RD SHARMA|Exercise Exercise|62 Videos

  • INDEFINITE INTEGRALS

    OBJECTIVE RD SHARMA|Exercise Chapter Test|30 Videos

  • INCREASING AND DECREASING FUNCTIONS

    OBJECTIVE RD SHARMA|Exercise Chapter Test|20 Videos

  • INTEGRALS

    OBJECTIVE RD SHARMA|Exercise Illustration|1 Videos

Similar Questions

Explore conceptually related problems

int(1)/(root(3)(x))dx

int(dx)/(1+root(3)(1+x))

"int(x-1)/(root(3)(x^(2)))dx

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

int(1)/(root(3)(x^(2)))dx

int(1)/(root(2)(x))dx

int(1)/(root(4)(x^(3)))dx

int(x+root(3)(x^(2))+root(6)(x))/(x(1+root(3)(x)))dx is equal to (i)(3)/(2)x(1+root(3)(x))(3)/(2)x^((2)/(3))+6tan^(-1)x^(6)+C( iii) (3)/(2)x^((2)/(3))+6tan^(-1)x^((1)/(6))+C( iv) (2)/(3)x^((2)/(3))+5tan^(-1)x^(6)+C

int(1+sqrt(x))/(1+root(3)(x))dx