What is the integral of e^x+4pi-x^e ?

The integral of e^x+4pi-x^e is e^x+4pix-(x^{e+1})/(e+1)+C

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integral of e^x+4pi-x^e

\int e^{x} + 4 π - x^{e} d x

e^{x} + 4 π x - \frac{x ^{e + 1}}{e + 1} + C

Solution steps

\int e^{x} + 4 π - x^{e} d x

Apply the Sum Rule:

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

= \int e^{x} d x + \int 4 π d x - \int x^{e} d x

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

\int 4 π d x = 4 π x

\int x^{e} d x = \frac{x ^{e + 1}}{e + 1}

= e^{x} + 4 π x - \frac{x ^{e + 1}}{e + 1}

Add a constant to the solution

= e^{x} + 4 π x - \frac{x ^{e + 1}}{e + 1} + C

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What is the integral of e^x+4pi-x^e ?
The integral of e^x+4pi-x^e is e^x+4pix-(x^{e+1})/(e+1)+C