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Step-by-step Solution

Solve the trigonometric integral $\int\sin\left(x\right)^4\cos\left(x\right)dx$

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Answer

$\frac{\sin\left(x\right)^{5}}{5}+C_0$

Step-by-step explanation

Problem to solve:

$\int\left(sin^4\left(x\right)cos\left(x\right)\right)dx$
1

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

$\begin{matrix}u=\sin\left(x\right) \\ du=\cos\left(x\right)dx\end{matrix}$
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Isolate $dx$ in the previous equation

$\frac{du}{\cos\left(x\right)}=dx$

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Answer

$\frac{\sin\left(x\right)^{5}}{5}+C_0$
$\int\left(sin^4\left(x\right)cos\left(x\right)\right)dx$

Main topic:

Trigonometric integrals

Related formulas:

2. See formulas

Time to solve it:

~ 0.04 seconds