First slide

Introduction to integration

Question

$\int {cosec}^{4} x d x =$

Easy

A

$\cot x + \frac{\cot^{3} x}{3} + c$
B

$\tan x \frac{\tan^{3} x}{3} + c$
C

$- \cot x - \frac{\cot^{3} x}{3} + c$
D

$- \tan x - \frac{\tan^{3} x}{3} + c$

Solution

$\begin{array}{l} I = \int {cosec}^{4} xdx = \int {cosec}^{2} x \cdot {cosec}^{2} xdx \\ = \int {cosec}^{2} x (1 + \cot^{2} x) dx \\ = \int {cosec}^{2} xdx + \int \cot^{2} x \cdot {cosec}^{2} xdx \\ = - \cot x - \frac{\cot^{3} x}{3} + c \end{array}$

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