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Step-by-step Solution

Integrate $\sec\left(2x\right)\tan\left(2x\right)$ from $0$ to $\frac{\pi }{6}$

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Answer

$\frac{1}{2}$

Step-by-step explanation

Problem to solve:

$\int_0^{\frac{\pi}{6}}\left(sec2x\:tan\:2x\right)dx$
1

Solve the integral $\int_{0}^{\frac{2}{\sqrt{3}}}\sec\left(2x\right)\tan\left(2x\right)dx$ applying u-substitution. Let $u$ and $du$ be

$\begin{matrix}u=2x \\ du=2dx\end{matrix}$
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Isolate $dx$ in the previous equation

$\frac{du}{2}=dx$

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Answer

$\frac{1}{2}$
$\int_0^{\frac{\pi}{6}}\left(sec2x\:tan\:2x\right)dx$

Main topic:

Definite integrals

Related formulas:

4. See formulas

Time to solve it:

~ 0.05 seconds