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

`inttan^(- 1)sqrt(x)dx`

Text Solution

Verified by Experts

Given:`inttan^(- 1)sqrt(x)dx`
`I=int tan^(- 1)sqrt(x)dx`
`I= x tan^(- 1)sqrt(x)-int (x)/(2(1+x)sqrtx)dx`
`I= x tan^(- 1)sqrt(x)-1/2int (sqrtx)/(1+x)dx`
Let `sqrtx=t implies (dx)/(2sqrtx)=dt implies dx=2tdt`
`I= x tan^(- 1)sqrt(x)-int (t^2)/(1+t^2)dt`
`I= x tan^(- 1)sqrt(x)-int dt+int 1/(1+t^2)dt`
`I= x tan^(- 1)sqrt(x)-sqrtx+tan^(-1)sqrt(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^(-1)sqrt((1-x)/(1+x))\ dx

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

Evaluate : (i) intsin^(-1)(3x-4x^(3))dx (ii) intsin^(-1)((2x)/(1+x^(2)))dx (iii) inttan^(-1)sqrt((1-x)/(1+x))dx (iv) intsin^(-1)sqrt((x)/(a+x))dx

If inttan^(-1)sqrtx dx=u tan^(-1)sqrtx-sqrtx+c, then u=

inttan^(- 1)sqrt((1-sinx)/(1+sinx))dx ,-pi/2

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

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

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

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