First slide

Introduction to integration

Question

If $\int \frac{1 - 5 \sin^{2} x}{\cos^{5} x \sin^{2} x} d x = \frac{f (x)}{\cos^{5} x} + C$ , then $f (x) :$

Easy

A

$- \cos e c x$
B

$\cos e c x$
C

$c o t x$
D

$- c o t x$

Solution

$\begin{array}{l} \int \frac{1 - 5 \sin^{2} x}{\cos^{5} x \sin^{2} x} d x = \int \frac{{cosec}^{2} x}{\cos^{5} x} d x - 5 \int \frac{1}{\cos^{5} x} d x \\ = - \frac{\cot x}{\cos^{5} x} + \int \cot x (- 5 \cos^{- 6} x) (- \sin x) d x - 5 \int \frac{1}{\cos^{5} x} d x \\ = - \frac{\cot x}{\cos^{5} x} + 5 \int \frac{d x}{\cos^{5} x} - 5 \int \frac{d x}{\cos^{5} x} + C \\ = - \frac{\cot x}{\cos^{5} x} + C \end{array}$
So $f (x) = - c o t x$

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