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\int\sec\left(2x\right)^4dx

Integrate sec(2x)^4

Answer

$\frac{1}{2}\left(\frac{2}{3}\tan\left(2x\right)+\frac{\sec\left(2x\right)^{3}\sin\left(2x\right)}{3}\right)+C_0$

Step-by-step explanation

Problem

$\int\sec\left(2x\right)^4dx$
1

Solve the integral $\int\sec\left(2x\right)^4dx$ applying u-substitution. Let $u$ and $du$ be

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

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Answer

$\frac{1}{2}\left(\frac{2}{3}\tan\left(2x\right)+\frac{\sec\left(2x\right)^{3}\sin\left(2x\right)}{3}\right)+C_0$
$\int\sec\left(2x\right)^4dx$

Main topic:

Trigonometric integrals

Used formulas:

2. See formulas

Time to solve it:

~ 0.38 seconds