What is the integral of xarcos(x) ?

The integral of xarcos(x) is ar(xsin(x)+cos(x))+C

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integral of xarcos(x)

\int x a r cos (x) d x

a r (x sin (x) + cos (x)) + C

Solution steps

\int x a r cos (x) d x

Take the constant out:

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

= a r \cdot \int x cos (x) d x

Apply Integration By Parts

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

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

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

= a r (x sin (x) - (- cos (x)))

Simplify

= a r (x sin (x) + cos (x))

Add a constant to the solution

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

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\int x \frac{d}{1} (x) d x

\int \frac{x e ^{x}}{e ^{x} - 3} d x

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