Answer
$-\frac{ln|cos(5θ)|}{5}+C$
Work Step by Step
$\int tan (5θ) dθ$
let $u=5θ$ $du= 5θ$
$dθ=\frac{1}{5}du$
$\int tan (5θ) dθ$
$=\frac{1}{5}\int tan (u)$ $du$
$=\frac{1}{5}(-ln|cos(u)|)+C$
$=-\frac{ln|cos(5θ)|}{5}+C$
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