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Step-by-step Solution

Trigonometric integral int(x*cos(3*x)*1)dx

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Answer

$\frac{1}{9}\left(3x\sin\left(3x\right)+\cos\left(3x\right)\right)+C_0$

Step-by-step explanation

Problem to solve:

$\int\left(x\cos3x\right)dx$
1

Any expression multiplied by $1$ is equal to itself

$\int x\cos\left(3x\right)dx$
2

Solve the integral $\int x\cos\left(3x\right)dx$ applying u-substitution. Let $u$ and $du$ be

$\begin{matrix}u=3x \\ du=3dx\end{matrix}$

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Answer

$\frac{1}{9}\left(3x\sin\left(3x\right)+\cos\left(3x\right)\right)+C_0$
$\int\left(x\cos3x\right)dx$

Main topic:

Trigonometric integrals

Used formulas:

5. See formulas

Time to solve it:

~ 0.79 seconds

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