What is the integral of (t^5+e^{3t}) ?

The integral of (t^5+e^{3t}) is (t^6)/6+1/3 e^{3t}+C

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integral of (t^5+e^{3t})

\int (t^{5} + e^{3 t}) d t

\frac{t ^{6}}{6} + \frac{1}{3} e^{3 t} + C

Solution steps

\int t^{5} + e^{3 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 t^{5} d t + \int e^{3 t} d t

\int t^{5} d t = \frac{t ^{6}}{6}

\int e^{3 t} d t = \frac{1}{3} e^{3 t}

= \frac{t ^{6}}{6} + \frac{1}{3} e^{3 t}

Add a constant to the solution

= \frac{t ^{6}}{6} + \frac{1}{3} e^{3 t} + C

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What is the integral of (t^5+e^{3t}) ?
The integral of (t^5+e^{3t}) is (t^6)/6+1/3 e^{3t}+C