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

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

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integral of 2sin(2t)+4t

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

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

Solution steps

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

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 t) d t + \int 4 t d t

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

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

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

Add a constant to the solution

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

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