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Step-by-step Solution

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

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Answer

$\frac{1}{16}\left(-4x\cos\left(4x\right)+\sin\left(4x\right)\right)+C_0$

Step-by-step explanation

Problem to solve:

$\int\left(x\sin4x\right)dx$
1

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

$\begin{matrix}u=4x \\ du=4dx\end{matrix}$
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Isolate $dx$ in the previous equation

$\frac{du}{4}=dx$

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Answer

$\frac{1}{16}\left(-4x\cos\left(4x\right)+\sin\left(4x\right)\right)+C_0$
$\int\left(x\sin4x\right)dx$

Main topic:

Trigonometric integrals

Used formulas:

4. See formulas

Time to solve it:

~ 0.75 seconds