What is the integral of xsin(x)+cos(x) ?

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

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integral of xsin(x)+cos(x)

\int x sin (x) + cos (x) d x

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

Solution steps

\int x sin (x) + cos (x) d x

Apply the Sum Rule:

\int f (x) \pm g (x) d x = \int f (x) d x \pm \int g (x) d x

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

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

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

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

Simplify

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

Add a constant to the solution

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

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\int e^{x^{9}} x^{8} d x

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