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

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

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integral of-xcos(pi-x)

\int - x cos (π - x) d x

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

Solution steps

\int - x cos (π - x) d x

Take the constant out:

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

= - \int x cos (π - x) d x

Rewrite using trig identities

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

Take the constant out:

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

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

Apply Integration By Parts

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

Use the common integral:

\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

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