First slide

Introduction to integration

Question

$\int \cos e c^{4} x d x =$

Easy

A

$- \tan x - \frac{\tan^{3} x}{3} + C$
B

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

$- c o t x - \frac{c o t^{3} x}{3} + C$
D

$- c o t x + \frac{c o t^{3} x}{3} + C$

Solution

$\int \cos e c^{4} x d x = \int \cos e c^{2} x \cos e c^{2} x d x = \int \cos e c^{2} x (1 + c o t^{2} x) d x = \int \cos e c^{2} x d x + \int \cos e c^{2} x c o t^{2} x d x = - c o t x - \frac{c o t^{3} x}{3} + C$

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