Home
Class 12
MATHS
intx^(-2//3)(1+x^(1//2))^(-5//3) dx is e...

`intx^(-2//3)(1+x^(1//2))^(-5//3)` dx is equal to

A

`3(1+x^(-1//2))^(-1//3)+C`

B

`3(1+x^(-1//2))^(-2//3)+C`

C

`3(1+x^(1//2))^(-2//3)+C`

D

None of the above

Text Solution

Verified by Experts

The correct Answer is:
B
`intx^(-2//3).{(x^(1//2))(x^(-1//2)+1)}^(-5//3)dx`
`=int x^(-2//3).x^(5//5).(x^(-1//2)+1)^(-5//3)dx`
`=intx^(-3//2).(x^(-1//2)+1)^(-5//3)dx`
`"Put "x^(-1//2)+1=t`
`therefore" "-(1)/(2)x^(-3//2)dx=dt`
Then,`" "-2int t^(-5//3)dt=-2.(t^(-2//3))/(-2//3)+C`
`=3(x^(-1//2)+1)^(-2//3)+C`
Promotional Banner

Topper's Solved these Questions

  • INTEGRATION

    MHTCET PREVIOUS YEAR PAPERS AND PRACTICE PAPERS|Exercise MHT CET Corner|30 Videos

  • INTEGRATION

    MHTCET PREVIOUS YEAR PAPERS AND PRACTICE PAPERS|Exercise MHT CET Corner|30 Videos

  • FACTORIZATION FORMULAE

    MHTCET PREVIOUS YEAR PAPERS AND PRACTICE PAPERS|Exercise EXERCISE 2|21 Videos

  • LINE

    MHTCET PREVIOUS YEAR PAPERS AND PRACTICE PAPERS|Exercise MHT CET Corner|3 Videos

Similar Questions

Explore conceptually related problems

int x^(-(2)/(3))(1+x^((1)/(2)))^(-(5)/(3))dx is equal to

int x^(-(2)/(3))(1+x^((1)/(2)))^(-(5)/(3))dx is equal to :

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

intx^(13//2)(1+x^(5//2))^(1//2)dx=

intx^3dx is equal to …

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

intx^(2)(1-x)^((5)/(2))dx

intx^(3)log x dx is equal to

intx^(1/3)sin(x^(4/3))dx