Home
Class 12
MATHS
Integrate the function sin^(-1)((2x)/(1+...

Integrate the function `sin^(-1)((2x)/(1+x^2))`

Text Solution

AI Generated Solution

To integrate the function \( \sin^{-1}\left(\frac{2x}{1+x^2}\right) \), we can follow these steps: ### Step 1: Substitution We know that \( \sin(2\theta) = \frac{2\tan(\theta)}{1+\tan^2(\theta)} \). Therefore, we can set: \[ \frac{2x}{1+x^2} = \sin(2\theta) \] This implies: ...
Promotional Banner

Topper's Solved these Questions

  • INTEGRALS

    NCERT|Exercise EXERCISE 7.10|10 Videos

  • INTEGRALS

    NCERT|Exercise EXERCISE 7.7|14 Videos

  • INTEGRALS

    NCERT|Exercise EXERCISE 7.9|22 Videos

  • DIFFERENTIAL EQUATIONS

    NCERT|Exercise EXERCISE 9.1|12 Videos

  • INVERSE TRIGONOMETRIC FUNCTIONS

    NCERT|Exercise MISCELLANEOUS EXERCISE|17 Videos

Similar Questions

Explore conceptually related problems

Integrate the functions x sin^(-1)x

Integrate the functions (sin^(-1)x)^(2)

integrate the function x sin x

Integrate the functions (sin^(2)x)/(1+cos x)

Integrate the functions (sin x)/((1+cos x)^(2))

Integrate the functions (e^(tan(-1)x))/(1+x^(2))

Integrate the functions (sin x)/(1+cos x)

Integrate the functions (e^(2x)-1)/(e^(2x)+1)

Integrate the functions xsqrt(1+2x^2)

Integrate the functions (sin^(8)-cos^(8)x)/(1-2sin^(2)x cos^(2)x)