What is the integral of cos(x)(2x) ?

The integral of cos(x)(2x) is 2(xsin(x)+cos(x))+C

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integral of cos(x)(2x)

\int cos (x) (2 x) d x

2 (x sin (x) + cos (x)) + C

Solution steps

\int cos (x) \cdot 2 x d x

Take the constant out:

\int a \cdot f (x) d x = a \cdot \int f (x) d x

= 2 \cdot \int cos (x) x d x

Apply Integration By Parts

: x sin (x) - \int sin (x) d x

= 2 (x sin (x) - \int sin (x) d x)

\int sin (x) d x = - cos (x)

= 2 (x sin (x) - (- cos (x)))

Simplify

= 2 (x sin (x) + cos (x))

Add a constant to the solution

= 2 (x sin (x) + cos (x)) + C

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What is the integral of cos(x)(2x) ?
The integral of cos(x)(2x) is 2(xsin(x)+cos(x))+C