First slide

Methods of integration

Question

$\int \frac{3 - 4 \tan x}{3 \tan x + 4} d x = \log (f (x)) + c t h e n f (x) = - - -$

Easy

A

$3 \sin x + 4 \cos x$
B

$4 \sin x + 3 \cos x$
C

$3 \sin x - 4 \cos x$
D

$4 \sin x - 3 \cos x$

Solution

$\int \frac{3 \cos x - 4 \sin x}{3 \sin x + 4 \cos x} d x$
$\begin{array}{l} Let 3 \sin x + 4 \cos x = f (x) \\ 3 \cos x - 4 \sin x = f^{'} (x) \end{array}$
$\begin{array}{l} \int \frac{f^{'} (x)}{f (x)} d x = \log (f (x)) + c \\ = \log (3 \sin x + 4 \cos x) + c \end{array}$

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