First slide

Methods of integration

Question

$\int (\sec x)^{n} \tan x d x is equal to$

Moderate

A

$\frac{- {(\sec x)}^{n + 1}}{n + 1} + C$
B

$\frac{{(\sec x)}^{n + 1}}{n + 1} + C$
C

$\frac{{(\sec x)}^{n}}{n} + C$
D

$- \frac{1}{n} {(\sec x)}^{n} + C$

Solution

$Let I = \int (\sec x)^{n} \tan x d x$
$I = \int (\sec x)^{n - 1} (\sec x \tan x) d x$
$Let \sec x = t$
$\begin{array}{l} \sec x \tan x d x = d t \\ I = \int t^{n - 1} d t \\ = \frac{t^{n}}{n} + C \\ = \frac{(\sec x)^{n}}{n} + C \end{array}$

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