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Step-by-step Solution

Integrate xcos(b*x)*1

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Answer

$x\frac{1}{b}\sin\left(bx\right)+\left(\frac{1}{b}\right)^2\cos\left(bx\right)+C_0$

Step-by-step explanation

Problem to solve:

$\int_{ }^{ }x\cos bx\:dx$
1

Any expression multiplied by $1$ is equal to itself

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

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

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

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Answer

$x\frac{1}{b}\sin\left(bx\right)+\left(\frac{1}{b}\right)^2\cos\left(bx\right)+C_0$

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$\int_{ }^{ }x\cos bx\:dx$

Main topic:

Integration by parts

Used formulas:

5. See formulas

Time to solve it:

~ 1.46 seconds