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

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

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integral of 2x-sin(x)

\int 2 x - sin (x) d x

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

Solution steps

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

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

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

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

Simplify

= x^{2} + cos (x)

Add a constant to the solution

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