What is the integral of 2sin(2x)+4x ?

The integral of 2sin(2x)+4x is -cos(2x)+2x^2+C

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integral of 2sin(2x)+4x

\int 2 sin (2 x) + 4 x d x

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

Solution steps

\int 2 sin (2 x) + 4 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 sin (2 x) d x + \int 4 x d x

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

\int 4 x d x = 2 x^{2}

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

Add a constant to the solution

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

What is the integral of 2sin(2x)+4x ?
The integral of 2sin(2x)+4x is -cos(2x)+2x^2+C