Home
Class 12
MATHS
The value of int(dx)/(x^(1/5)(1+x^(4/5))...

The value of `int(dx)/(x^(1/5)(1+x^(4/5))^(1/2)` is

A

`sqrt(1+x^(4//5))+C`

B

`(5)/(2)sqrt(1+x^(4//5))+C`

C

`x^(4//5)sqrt(1+x^(4//5))+C`

D

none of these

Text Solution

Verified by Experts

The correct Answer is:
b
Let I `=int(1)/(x^(1//5)(1+x^(4//5))^(1//2))dx`
`rArrI=(5)/(4)int(1)/((1+x^(4//5))^(1//2))((4)/(5)x^(-1//5))dx`
`rArrI=(5)/(4)int(1)/((1+x^(4//5))^(1//2))d(1+x^(4//5))=(5)/(2)(1+x^(4//5))^(1//2)+C`
Promotional Banner

Topper's Solved these Questions

  • INDEFINITE INTEGRALS

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

  • INDEFINITE INTEGRALS

    OBJECTIVE RD SHARMA ENGLISH|Exercise Exercise|61 Videos

  • INDEFINITE INTEGRALS

    OBJECTIVE RD SHARMA ENGLISH|Exercise Chapter Test|30 Videos

  • INCREASING AND DECREASING FUNCTIONS

    OBJECTIVE RD SHARMA ENGLISH|Exercise Chapter Test|18 Videos

  • INVERSE TRIGONOMETRIC FUNCTIONS

    OBJECTIVE RD SHARMA ENGLISH|Exercise Chapter Test|30 Videos

Similar Questions

Explore conceptually related problems

Evaluate: int(dx)/(x^2(1+x^5)^(4/5))

Evaluate: int(dx)/(x^2(1+x^5)^(4/5))

int(dx)/((x+1)^(6/5)(x-3)^(4/5))=

The value of int_(1)^(2) (dx)/(x(1+x^(4)) is

The value of int_(1)^(2)(x^(2)+1)/(x^(4)-x^(2)+1)log(1+x-1/x)dx is

The value of int((x^(2)+1))/((x^(4)-x^(2)+1)cot^(-1)(x-(1)/(x)))dx will be

The value of int_(-1)^(1)(sin^(-1)x+(x^(5)+x^(3)-1)/(cos^(2)x))dx is equal to

int(1)/(x^(1//2)(1+x^(2))^(5//4))dx is equal to

Find the value of int(1)/[(x-1)^3(x+2)^5]^(1/4)dx

The value of integral int1/[(x-3)^(3)(x+2)^(5)]^(1//4)dx is