What is the integral of (3+3^x+x^3) ?

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

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integral of (3+3^x+x^3)

\int (3 + 3^{x} + x^{3}) d x

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

Solution steps

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

\int 3 d x = 3 x

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

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

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

Add a constant to the solution

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

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