Mathematics

Mathematics

Problem

∫dx(x2+1)(x2+4)=\int \frac{dx}{(x^2+1)(x^2+4)} = (a) 13tan⁡−1x−13tan⁡−1x2+c\frac{1}{3}\tan^{-1}x-\frac{1}{3}\tan^{-1}\frac{x}{2}+c (b) 13tan⁡−1x+13tan⁡−1x2+c\frac{1}{3}\tan^{-1}x+\frac{1}{3}\tan^{-1}\frac{x}{2}+c (c) 13tan⁡−1x−16tan⁡−1x2+c\frac{1}{3}\tan^{-1}x-\frac{1}{6}\tan^{-1}\frac{x}{2}+c (d) tan⁡−1x−2tan⁡−1x2+c\tan^{-1}x-2\tan^{-1}\frac{x}{2}+c (a) 13tan⁡−1x−13tan⁡−1x2+c\frac{1}{3}\tan^{-1}x-\frac{1}{3}\tan^{-1}\frac{x}{2}+c (b) 13tan⁡−1x+13tan⁡−1x2+c\frac{1}{3}\tan^{-1}x+\frac{1}{3}\tan^{-1}\frac{x}{2}+c (c) 13tan⁡−1x−16tan⁡−1x2+c\frac{1}{3}\tan^{-1}x-\frac{1}{6}\tan^{-1}\frac{x}{2}+c (d) tan⁡−1x−2tan⁡−1x2+c\tan^{-1}x-2\tan^{-1}\frac{x}{2}+c

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