First slide

Methods of integration

Question

$\int e^{x} (\frac{2 \tan x}{1 + \tan x} + \cot^{2} (x + \frac{π}{4})) d x is equal to$

Moderate

A

$e^{x} \tan (\frac{π}{4} - x) + c$
B

$e^{x} \tan (x - \frac{π}{4}) + c$
C

$e^{x} \tan (\frac{3 π}{4} - x) + c$
D

$None of these$

Solution

$\begin{array}{l} \int e^{x} (\frac{2 \tan x}{1 + \tan x} + \tan^{2} (x - \frac{π}{4})) dx \\ = \int e^{x} (\tan (x - \frac{π}{4}) + \sec^{2} (x - \frac{π}{4})) dx \\ = e^{x} \tan (x - \frac{π}{4}) + c \end{array}$

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