Ask Questions, Get Answers

Home  >>  JEEMAIN and NEET  >>  Mathematics  >>  Class12  >>  Integral Calculus

Integrate : $\int x^{\tan x }\bigg[\large\frac{\tan x}{x} $$+ \sec^2 x . \log x \bigg]$$dx$

$(a)\;\tan x +c \\(b)\; x^{\tan x}+c \\(c)\; \frac{[x \cot x]^2}{2}+c \\ (d)\;None$

1 Answer

$x^{\tan x}=t$
differentiate with respect to x by taking log
$\tan x \log x =\log t$
$x^{\tan x} [\large\frac{\tan x}{x} $$+ \sec^2 x . \log x]$$dx=dt$
$\int t.dt$
=> $\large\frac{t^2}{2}$$+c$
=> $\Large\frac{[x ^{\tan x}]^2}{2}$$+c$
Hence d is the correct answer.
answered Dec 31, 2013 by meena.p