Home
Class 12
MATHS
Evaluate: int(x^2tan^(-1)x^3)/(1+x^6)dx...

Evaluate: `int(x^2tan^(-1)x^3)/(1+x^6)dx`

A

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

B

`log|tan^(-1)x^(3)|+C`

C

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

D

none of these

Text Solution

Verified by Experts

The correct Answer is:
C
Put `tan^(-1)x^(3)=t and(3x^(2))/((1+x^(6)))dx=dt`.
`:." "I=(1)/(3)intdt=(1)/(6)(tan^(-1)x^(3))^(2)+C`.
Promotional Banner

Topper's Solved these Questions

  • METHODS OF INTEGRATION

    RS AGGARWAL|Exercise Exercise 13B|34 Videos

  • METHODS OF INTEGRATION

    RS AGGARWAL|Exercise Exercise 13C|87 Videos

  • METHODS OF INTEGRATION

    RS AGGARWAL|Exercise EXERCISE 13A SHORT ANSWER QUESTIONS|92 Videos

  • MATRICES

    RS AGGARWAL|Exercise Exercise 5F|21 Videos

  • PROBABILITY

    RS AGGARWAL|Exercise Exercise 29 B|2 Videos

Similar Questions

Explore conceptually related problems

int(x^2tan^-1x^3)/(1+x^6)dx

Evaluate: int(x^(2)tan^(-1)x^(3))/(1+x^(6))dx

int(x^(2)tan^(-1)(x^(3)))/(1+x^(6))dx

Evaluate: int(x tan^(-1)x^(2))/(1)dx

Evaluate int (x+tan^(-1)x)dx

Evaluate: int(x^(2)"tan"^(-1)x^(3))/(1+x^(6))dx

int(6x^(2)tan^(-1)(x^(3)))/(1+x^(6))dx=

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