What is the integral of-4sin(4t)+1 ?

The integral of-4sin(4t)+1 is cos(4t)+t+C

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integral of-4sin(4t)+1

\int - 4 sin (4 t) + 1 d t

cos (4 t) + t + C

Solution steps

\int - 4 sin (4 t) + 1 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 4 sin (4 t) d t + \int 1 d t

\int 4 sin (4 t) d t = - cos (4 t)

\int 1 d t = t

= - (- cos (4 t)) + t

Simplify

= cos (4 t) + t

Add a constant to the solution

= cos (4 t) + t + C