CBSE

MATHEMATICS · Single correct · CBSE · Mathematics · Integrals · Integrals

Problem

\int \frac{1}{(x^2+a^2)(x^2+b^2)}\,dx =

(a)

\frac{1}{(a^2-b^2)}\left[\frac{1}{b}\tan^{-1}\left(\frac{x}{b}\right)-\frac{1}{a}\tan^{-1}\left(\frac{x}{a}\right)\right]+c

(b)

\frac{1}{(b^2-a^2)}\left[\frac{1}{b}\tan^{-1}\left(\frac{x}{b}\right)-\frac{1}{a}\tan^{-1}\left(\frac{x}{a}\right)\right]+c

(c)

\frac{1}{b}\tan^{-1}\left(\frac{x}{b}\right)-\frac{1}{a}\tan^{-1}\left(\frac{x}{a}\right)+c

(d)

\frac{1}{a}\tan^{-1}\left(\frac{x}{a}\right)-\frac{1}{b}\tan^{-1}\left(\frac{x}{b}\right)+c