First slide

Methods of integration

Question

$\int \frac{e^{\cot x}}{\sin^{2} x} (2 \log (\cos e c x) + \sin 2 x) d x$

Moderate

A

$2 e^{\cot x} \log (\cos e c x) + C$
B

$e^{\cot x} \log (\cos e c x) + C$
C

$- 2 e^{\cot x} \log (\cos e c x) + C$
D

$- 2 e^{\cot x} \log (\cos x) + C$

Solution

$\begin{array}{l} \cot x = t {cosec}^{2} x d x = d t \\ - \int e^{t} (2 \log (\sqrt{t^{2} + 1}) + \frac{2 t}{1 + t^{2}}) d t \\ = - e^{t} \log (t^{2} + 1) + C = - e^{\cot x} \log (1 + \cot^{2} x) + C \\ = - 2 e^{\cot x} \log (\cos e c x) + C \end{array}$

Get Instant Solutions

When in doubt download our app. Now available Google Play Store- Doubts App

Recieve an sms with download link

Doubts App

OR

SCAN ME

Doubts App

Doubts App