Step-by-step Solution

Integral of xsin(4*x)*1

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

Step-by-step explanation

Problem to solve:

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

Any expression multiplied by $1$ is equal to itself

$\int x\sin\left(4x\right)dx$
2

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

$\begin{matrix}u=4x \\ du=4dx\end{matrix}$

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

Main topic:

Integration by parts

~ 1.05 seconds