What is the integral of xcos(-x) ?

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

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integral of xcos(-x)

\int x cos (- x) d x

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

Solution steps

\int x cos (- x) d x

Simplify

x cos (- x) : x cos (x)

= \int x cos (x) d x

Apply Integration By Parts

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

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

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

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

Simplify

= x sin (x) + cos (x)

Add a constant to the solution

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

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