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

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

Text Solution

Verified by Experts

`"Let I " =int(x^(2)"sin"^(-1)x^(3))/(1+x^(6))dx`
`=int"tan"^(-1)x^(3).((x^(2)dx)/(1+x^(6)))`
`"Let tan"^(-1) x^(3)=t`
`rArr (1)/(1+x^(6)).3x^(2)=(dt)/(dx)rArr(x^(2)dx)/(1+x^(6))=(dt)/(3)`
`I=intt.(dt)/(3)=1/6t^(2)+c`
` =1/6("tan"^(-1)x^(3))^(2)+c.`
Promotional Banner

Topper's Solved these Questions

  • INTEGRATION

    NAGEEN PRAKASHAN ENGLISH|Exercise Exercise 7a|14 Videos

  • INTEGRATION

    NAGEEN PRAKASHAN ENGLISH|Exercise Exercise 7b|26 Videos

  • DIFFERENTIAL EQUATIONS

    NAGEEN PRAKASHAN ENGLISH|Exercise Miscellaneous Exercise|18 Videos

  • INVERES TRIGONOMETRIC FUNCTIONS

    NAGEEN PRAKASHAN ENGLISH|Exercise Miscellaneous Exercise (prove That )|9 Videos

Similar Questions

Explore conceptually related problems

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

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

Evaluate : int_(0)^(1)((tan^(-1)x)^(2))/(1+x^(2))dx

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

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

Evaluate int(3x^(2)"tan"(1)/(x)-x"sec"^(2)(1)/(x))dx .

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

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

Evaluate: int(x^(1/2))/(1+x^(3/4))dx

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