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 x cos (x) - sin (x) d x

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

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

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

\int u^{- 4} d u

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