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

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

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integral of xcos(x)-sin(x)

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

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

Solution steps

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

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

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

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

Simplify

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

Add a constant to the solution

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

\int \frac{16}{x} d x

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\int \frac{x}{4 + 25 x ^{2}} d x

\int u^{- 4} d u

\int \frac{v}{v + 1} d v

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