What is the integral of x^3+3^x+e^3 ?

The integral of x^3+3^x+e^3 is (x^4)/4+(3^x)/(ln(3))+e^3x+C

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integral of x^3+3^x+e^3

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

\frac{x ^{4}}{4} + \frac{3 ^{x}}{ln ( 3 )} + e^{3} x + C

Solution steps

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

\int x^{3} d x = \frac{x ^{4}}{4}

\int 3^{x} d x = \frac{3 ^{x}}{ln ( 3 )}

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

= \frac{x ^{4}}{4} + \frac{3 ^{x}}{ln ( 3 )} + e^{3} x

Add a constant to the solution

= \frac{x ^{4}}{4} + \frac{3 ^{x}}{ln ( 3 )} + e^{3} x + C

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What is the integral of x^3+3^x+e^3 ?
The integral of x^3+3^x+e^3 is (x^4)/4+(3^x)/(ln(3))+e^3x+C