First slide

Introduction to integration

Question

$\int e^{\tan x} (\sin x - \sec x) d x =$

Moderate

A

$e^{\tan x} . \cos x + C$
B

$e^{\tan x} . \sin x + C$
C

$- e^{\tan x} . \cos x + C$
D

$e^{\tan x} . \sec x + C$

Solution

$\begin{array}{l} \int e^{\tan} \sin x d x - \int e^{\tan x} \sec x d x \\ (by parts) \\ = - \cos x e^{\tan x} + \int \cos x e^{\tan x} \cdot \sec^{2} x d x - \int e^{\tan x} \sec x d x \\ = - \cos x \cdot e^{\tan x} + C \end{array}$

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