({logtan}\theta - \frac{1}{2}\tan^{2}\theta + c) | MATH - INTEGRATION BY SUBSTITUTION | SolveeIt

${logtan}\theta - \frac{1}{2}\tan^{2}\theta + c$

${logtan}\theta + \frac{1}{2}\tan^{2}\theta + c$

$\int_{}^{}{\frac{1}{\cos^{- 1}x.\sqrt{1 - x^{2}}}dx =}$

$\log(\cos^{- 1}x) + c$

None of these

Answer

${logtan}\theta + \frac{1}{2}\tan^{2}\theta + c$

Explanation

$\int_{}^{}{\frac{f(x)\mspace{6mu} dx}{{logsin}x} = {loglogsin}x}$

Put $f(x) =$ then it reduces to

$\sin x$

Now again, put $\cos x$ then its reduced form is

$- 2 t d t = d u$ ${logsin}x$

Question: \({logtan}\theta - \frac{1}{2}\tan^{2}\theta + c\)...