What is the integral of cos(5t)+t^4 ?

The integral of cos(5t)+t^4 is 1/5 sin(5t)+(t^5)/5+C

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integral of cos(5t)+t^4

\int cos (5 t) + t^{4} d t

\frac{1}{5} sin (5 t) + \frac{t ^{5}}{5} + C

Solution steps

\int cos (5 t) + t^{4} 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 cos (5 t) d t + \int t^{4} d t

\int cos (5 t) d t = \frac{1}{5} sin (5 t)

\int t^{4} d t = \frac{t ^{5}}{5}

= \frac{1}{5} sin (5 t) + \frac{t ^{5}}{5}

Add a constant to the solution

= \frac{1}{5} sin (5 t) + \frac{t ^{5}}{5} + C

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What is the integral of cos(5t)+t^4 ?
The integral of cos(5t)+t^4 is 1/5 sin(5t)+(t^5)/5+C