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

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

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integral of 2x-cos(x)

\int 2 x - cos (x) d x

x^{2} - sin (x) + C

Solution steps

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

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

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

= x^{2} - sin (x)

Add a constant to the solution

= x^{2} - sin (x) + C