What is the integral of x-2sin(x) ?

The integral of x-2sin(x) is (x^2)/2+2cos(x)+C

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integral of x-2sin(x)

integral

x - 2 sin (x)

\frac{x ^{2}}{2} + 2 cos (x) + C

Solution steps

\int x - 2 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 d x - \int 2 sin (x) d x

\int x d x = \frac{x ^{2}}{2}

\int 2 sin (x) d x = - 2 cos (x)

= \frac{x ^{2}}{2} - (- 2 cos (x))

Simplify

= \frac{x ^{2}}{2} + 2 cos (x)

Add a constant to the solution

= \frac{x ^{2}}{2} + 2 cos (x) + C

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