∫((√x2+1)[log(x2+1)-2log x]/x4)dxis equal to

Question

∫((√x2+1)[log(x2+1)-2log x]/x4)dxis equal to (A) (1/3)(1+(1/x2))1/2[log(1+(1/x2)+(2/3)]+c (B) -(1/3)(1+(1/x2))3/2[log(1+(1/x2)-(2/3)]+c (C) (2/3)(1+(1/x2))3/2[log(1+(1/x2)+(2/3)]+c (D) none of these

Tardigrade Admin · Accepted Answer

Correct answer is (b) -(1/3)(1+(1/x2))3/2[log(1+(1/x2)-(2/3)]+c

Q. $\int \frac{( x ^{2} + 1 ) [ l o g ( x ^{2} + 1 ) - 2 l o g x ]}{x ^{4}} d x$ is equal to

$\frac{1}{3} (1 + \frac{1}{x ^{2}})^{1/2} [l o g (1 + \frac{1}{x ^{2}} + \frac{2}{3}] + c$

$- \frac{1}{3} (1 + \frac{1}{x ^{2}})^{3/2} [l o g (1 + \frac{1}{x ^{2}} - \frac{2}{3}] + c$

$\frac{2}{3} (1 + \frac{1}{x ^{2}})^{3/2} [l o g (1 + \frac{1}{x ^{2}} + \frac{2}{3}] + c$

none of these

Correct answer is (b) $- \frac{1}{3} (1 + \frac{1}{x ^{2}})^{3/2} [l o g (1 + \frac{1}{x ^{2}} - \frac{2}{3}] + c$

Q. ∫x4(x2+1)​[log(x2+1)−2logx]​dxis equal to

31​(1+x21​)1/2[log(1+x21​+32​]+c

−31​(1+x21​)3/2[log(1+x21​−32​]+c

32​(1+x21​)3/2[log(1+x21​+32​]+c