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

`(1)/(2)log_(e)((x^(3)+1)^(2))/(|x^(3)|)+c`

B

`log_(e)(|x^(3)+1|)/(x^(2))+c`

C

`(1)/(2)log_(e)(|x^(3)+1|)/(x^(2))+C`

D

`log_(e)|(x^(3)+1)/(x)|+C`

Text Solution

Verified by Experts

The correct Answer is:
D
`int(2x^(3)-1)/(x^(4)+x)=int(2x^(3))/(x^(4)+x)-int(1)/(x^(4)+x)dx=(2)/(3)int(3x^(2))/(x^(3)+x)-int(1)/(x.(x^(3)+1))xx(x^(2))/(x^(2))dx=(2)/(3)log(x^(3)H)-(1)/(3)int(dt)/(t(t+1))`
`("put "x^(3)=t)`
`(2)/(3)log(x(3)+1)-(1)/(3)int((1)/(t)-(1)/(t+1))dt`
`(2)/(3)log(x^(3)+1)-(1)/(3)[logt-log(t+1)]+c=(2)/(3)log(x^(3)+1)-(1)/(3)log((x^(3))/(1+x^(3)))+c=(1)/(3)log|(x^(3)+1)^(2)(x^(3))/(1+x^(3))|+c`
`(1)/(3)log|((1+x^(3))/(x^(3)))^(3)|+c," "log|(1+x^(3))/(x)|`
Promotional Banner

Topper's Solved these Questions

  • JEE MAIN REVISION TEST- 16

    VMC MODULES ENGLISH|Exercise MATHEMATICS (SECTION 2)|5 Videos

  • JEE MAIN REVISION TEST 8 (2020)

    VMC MODULES ENGLISH|Exercise MATHEMATICS ( SECTION 2 )|5 Videos

  • JEE MAIN REVISION TEST- 24

    VMC MODULES ENGLISH|Exercise MATHEMATICS (SECTION - 2)|5 Videos

Similar Questions

Explore conceptually related problems

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

int|x|^(3) dx is equal to

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

int_(1//3)^(3)(1)/(x)log_(e)(|(x+x^(2)-1)/(x-x^(2)+1)|)dx is equal to

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

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

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

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

If int_(0)^(x)((t^(3)+t)dt)/((1+3t^(2)))=f(x) , then int_(0)^(1)f^(')(x) dx is equal to

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