First slide

Introduction to integration

Question

$If I = \int \frac{\log (\cos x)}{\cos^{2} x}, then I equals$

Moderate

A

$\tan x \log \cos x + \tan x - x + C$
B

$\tan x \log \cos x - \tan x + x^{2} + C$
C

$\tan x \log \cos x - \cot x + x + C$
D

$\tan x \log \cos x + \cot x - x + C$

Solution

$\begin{array}{l} I = \int \sec^{2} xlog \cos xdx \\ = \tan xlog \cos x - \int \tan x (- \tan x) dx \\ = \tan xlog \cos x + \tan x - x + C \end{array}$

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