What is the integral of (2^x+4e^x+x^3+5) ?

The integral of (2^x+4e^x+x^3+5) is (2^x}{ln(2)}+4e^x+\frac{x^4)/4+5x+C

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integral of (2^x+4e^x+x^3+5)

\int (2^{x} + 4 e^{x} + x^{3} + 5) d x

\frac{2 ^{x}}{ln ( 2 )} + 4 e^{x} + \frac{x ^{4}}{4} + 5 x + C

Solution steps

\int 2^{x} + 4 e^{x} + x^{3} + 5 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 2^{x} d x + \int 4 e^{x} d x + \int x^{3} d x + \int 5 d x

\int 2^{x} d x = \frac{2 ^{x}}{ln ( 2 )}

\int 4 e^{x} d x = 4 e^{x}

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

\int 5 d x = 5 x

= \frac{2 ^{x}}{ln ( 2 )} + 4 e^{x} + \frac{x ^{4}}{4} + 5 x

Add a constant to the solution

= \frac{2 ^{x}}{ln ( 2 )} + 4 e^{x} + \frac{x ^{4}}{4} + 5 x + C

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What is the integral of (2^x+4e^x+x^3+5) ?
The integral of (2^x+4e^x+x^3+5) is (2^x}{ln(2)}+4e^x+\frac{x^4)/4+5x+C