Home
Class 12
MATHS
Evaluate: inttan^(-1)(sqrt(x))\ dx...

Evaluate: `inttan^(-1)(sqrt(x))\ dx`

Text Solution

Verified by Experts

Let `I=int tan ^{-1} sqrt{x} d x`
` =int tan ^{-1} sqrt{x} cdot II _{text {I }} d x`
` =tan ^{-1} sqrt{x}, x-int frac{1}{1+x}, x d x`
` =x tan ^{-1} sqrt{x}-int frac{1+x-1}{1+x} d x`
` =x tan ^{-1} sqrt{x}-int frac{1+x}{1+x} d x+int frac{1}{1+x} d x`
` =x tan ^{-1} sqrt{x}-x+log |1+x|+c`
Promotional Banner

Topper's Solved these Questions

  • INCREASING AND DECREASING FUNCTION

    RD SHARMA|Exercise Solved Examples And Exercises|232 Videos

  • INVERSE TRIGONOMETRIC FUNCTION

    RD SHARMA|Exercise Solved Examples And Exercises|523 Videos

Similar Questions

Explore conceptually related problems

Evaluate: inttan^-1xdx

Evaluate: inttan^-1sqrt(sqrt(x)-1)dx

Evaluate: inttan^(-1)sqrt((1-x)/(1+x))\ dx

Evaluate: inttan^(-1)(x/a)dx .

Evaluate: int(1)/(sqrt(x)+x)dx

Evaluate: int(1)/(1+sqrt(x))dx

inttan^-1(x/sqrt(1+x^2))dx

Evaluate: inttan^(-1){sqrt(((1-sinx)/(1+sinx)))} dx , -pi//2

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

Evaluate: inttan^-1sqrt((1-x)/(1+x))dx