What is the integral of sin(t)+3cos(t) ?

The integral of sin(t)+3cos(t) is -cos(t)+3sin(t)+C

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integral of sin(t)+3cos(t)

\int sin (t) + 3 cos (t) d t

- cos (t) + 3 sin (t) + C

Solution steps

\int sin (t) + 3 cos (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 sin (t) d t + \int 3 cos (t) d t

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

\int 3 cos (t) d t = 3 sin (t)

= - cos (t) + 3 sin (t)

Add a constant to the solution

= - cos (t) + 3 sin (t) + C

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What is the integral of sin(t)+3cos(t) ?
The integral of sin(t)+3cos(t) is -cos(t)+3sin(t)+C