What is the integral of 3xe^{3z}+5 ?

The integral of 3xe^{3z}+5 is 5z+xe^{3z}+C

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integral of 3xe^{3z}+5

\int 3 x e^{3 z} + 5 d z

5 z + x e^{3 z} + C

Solution steps

\int 3 x e^{3 z} + 5 d z

Apply the Sum Rule:

\int f (x) \pm g (x) d x = \int f (x) d x \pm \int g (x) d x

= \int 5 d z + \int 3 x e^{3 z} d z

\int 5 d z = 5 z

\int 3 x e^{3 z} d z = x e^{3 z}

= 5 z + x e^{3 z}

Add a constant to the solution

= 5 z + x e^{3 z} + C

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