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Step-by-step Solution

Integrate tan(5*x)

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Answer

$-\frac{1}{5}\ln\left(\cos\left(5x\right)\right)+C_0$

Step-by-step explanation

Problem to solve:

$\int\tan\left(5x\right)dx$
1

Solve the integral $\int\tan\left(5x\right)dx$ applying u-substitution. Let $u$ and $du$ be

$\begin{matrix}u=5x \\ du=5dx\end{matrix}$
2

Isolate $dx$ in the previous equation

$\frac{du}{5}=dx$

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Answer

$-\frac{1}{5}\ln\left(\cos\left(5x\right)\right)+C_0$
$\int\tan\left(5x\right)dx$

Main topic:

Integration by substitution

Used formulas:

3. See formulas

Time to solve it:

~ 0.43 seconds