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Step-by-step Solution

Trigonometric integral int(x^2*cos(x)*1)dx

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asin
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Answer

$x^2\sin\left(x\right)-2\left(-x\cos\left(x\right)+\sin\left(x\right)\right)+C_0$

Step-by-step explanation

Problem to solve:

$\int\left(x^2cos\:x\:\right)dx$
1

Any expression multiplied by $1$ is equal to itself

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

Use the integration by parts theorem to calculate the integral $\int x^2\cos\left(x\right)dx$, using the following formula

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

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Answer

$x^2\sin\left(x\right)-2\left(-x\cos\left(x\right)+\sin\left(x\right)\right)+C_0$
$\int\left(x^2cos\:x\:\right)dx$

Main topic:

Trigonometric integrals

Used formulas:

5. See formulas

Time to solve it:

~ 0.79 seconds

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