What is the integral of asin(t)+cos(kt) ?

The integral of asin(t)+cos(kt) is -acos(t)+1/k sin(kt)+C

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integral of asin(t)+cos(kt)

\int a sin (t) + cos (k t) d t

- a cos (t) + \frac{1}{k} sin (k t) + C

Solution steps

\int a sin (t) + cos (k 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 a sin (t) d t + \int cos (k t) d t

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

\int cos (k t) d t = \frac{1}{k} sin (k t)

= - a cos (t) + \frac{1}{k} sin (k t)

Add a constant to the solution

= - a cos (t) + \frac{1}{k} sin (k t) + C

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What is the integral of asin(t)+cos(kt) ?
The integral of asin(t)+cos(kt) is -acos(t)+1/k sin(kt)+C