First slide

Methods of integration

Question

$\int \frac{\sec x}{a \cos x + b \sin x} d x =$

Easy

A

$\frac{1}{a} \log | a \cot x + b | + C$
B

$a \log | a + b \tan x | + C$
C

$b \log | a + b \tan x | + C$
D

$\frac{1}{b} \log | a + b \tan x | + C$

Solution

$\int \frac{\sec^{2} x}{a + b \tan x} d x$
$= \frac{1}{b} \int \frac{b \sec^{2} x}{a + b \tan x} d x$

$= \frac{1}{b} \log | a + b \tan x | + c$

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