What is the integral of-2xcos(x) ?

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

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integral of-2xcos(x)

\int - 2 x cos (x) d x

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

Solution steps

\int - 2 x cos (x) d x

Take the constant out:

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

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

Apply Integration By Parts

= - 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

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