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Step-by-step Solution

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

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ln
log
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sin
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csc

asin
acos
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acot
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acsc

sinh
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sech
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asinh
acosh
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Answer

$x\sin\left(x\right)+\cos\left(x\right)+C_0$

Step-by-step explanation

Problem to solve:

$\int x\cdot \cos\left(x\right)dx$
1

Use the integration by parts theorem to calculate the integral $\int x\cos\left(x\right)dx$, using the following formula

$\displaystyle\int u\cdot dv=u\cdot v-\int v \cdot du$
2

First, identify $u$ and calculate $du$

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

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Answer

$x\sin\left(x\right)+\cos\left(x\right)+C_0$
$\int x\cdot \cos\left(x\right)dx$

Main topic:

Integration by parts

Time to solve it:

~ 1.02 seconds

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