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

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

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integral of sin(x)-xcos(x)

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

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

Solution steps

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

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

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

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

Simplify

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

Add a constant to the solution

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

\int 1 + y e^{(x y)} d x

\int u u + 4 d u

\frac{1}{( 3 + t ) ^{2}}

\frac{d}{d x} ((x - 5) (5 x + 4))

\frac{\partial}{\partial y} (x ln (x^{2} + y^{2}))

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