Home
Class 12
MATHS
Evaluate: int0^1(x t a n^(-1)x)/((1+x^2)...

Evaluate: `int_0^1(x t a n^(-1)x)/((1+x^2)^(3//2))dx`

Text Solution

AI Generated Solution

To evaluate the integral \[ I = \int_0^1 \frac{x \tan^{-1}(x)}{(1+x^2)^{3/2}} \, dx, \] we will use the substitution \( x = \tan(\theta) \). ...
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: int1/(sqrt(t a n^(-1)x)(1+x^2))dx

Evaluate: int5^(x+t a n^(-1)x)((x^2+2)/(x^2+1))dx

Evaluate: int_0^1sin^(-1)((2x)/(1+x^2))dx

Evaluate: int_0^1sin^(-1)((2x)/(1+x^2))dx

Evaluate: int_(0)^(1//2) (sin^(-1)x)/((1-x^(2))^(3//2)) dx

Evaluate: int_0^(1)sin^(-1)((2x)/(1+x^2))dx

Evaluate: int_0^(1/2)(xsin^(-1)x)/(sqrt(1-x^2))dx

Evaluate: int_1^3 1/(x^2(x+1))dx

Evaluate: int_1^3 1/(x^2(x+1))dx

Evaluate: int_0^1x(1-x)^n dx