What is the integral of 20cos(10t+pi/6)+2 ?

The integral of 20cos(10t+pi/6)+2 is 2sin(10t+pi/6)+2t+C

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integral of 20cos(10t+pi/6)+2

\int 20 cos (10 t + \frac{π}{6}) + 2 d t

2 sin (10 t + \frac{π}{6}) + 2 t + C

Solution steps

\int 20 cos (10 t + \frac{π}{6}) + 2 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 20 cos (10 t + \frac{π}{6}) d t + \int 2 d t

\int 20 cos (10 t + \frac{π}{6}) d t = 2 sin (10 t + \frac{π}{6})

\int 2 d t = 2 t

= 2 sin (10 t + \frac{π}{6}) + 2 t

Add a constant to the solution

= 2 sin (10 t + \frac{π}{6}) + 2 t + C

What is the integral of 20cos(10t+pi/6)+2 ?
The integral of 20cos(10t+pi/6)+2 is 2sin(10t+pi/6)+2t+C