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

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

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integral of-cos(x)x

\int - cos (x) x d x

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

Solution steps

\int - cos (x) x d x

Take the constant out:

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

= - \int cos (x) 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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