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Step-by-step Solution

Trigonometric integral int(sec(2*x)*tan(2*x)*1)dx&0&pi/6

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Answer

$0.5$

Step-by-step explanation

Problem to solve:

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

Any expression multiplied by $1$ is equal to itself

$\int_{0}^{\frac{2}{\sqrt{3}}}\tan\left(2x\right)\sec\left(2x\right)dx$
2

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

$\begin{matrix}u=\sec\left(2x\right) \\ du=2\sec\left(2x\right)\tan\left(2x\right)dx\end{matrix}$

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Answer

$0.5$
$\int_0^{\frac{\pi}{6}}\left(sec2x\:tan\:2x\right)dx$

Main topic:

Trigonometric integrals

Used formulas:

3. See formulas

Time to solve it:

~ 0.89 seconds