∫cos x3+4sin xdx Let 3+4sin x=zcos xdx=dz4 ∫14zdz =14ln|z|+c =14ln|3+4sin x|+c ...

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Integration of Trigonometric Functions

∫cos xdx/3+4s...

Question

$\int \frac{cos x d x}{3 + 4 sin x}$

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Solution

$\int \frac{cos x}{3 + 4 sin x} d x$
Let $3 + 4 sin x = z ⟹ cos x d x = \frac{d z}{4}$
$\int \frac{1}{4 z} d z$
$= \frac{1}{4} ln | z | + c$
$= \frac{1}{4} ln | 3 + 4 sin x | + c$

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