What is the integral of x^{3/2}-3^x+3x^3 ?

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

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integral of x^{3/2}-3^x+3x^3

\int x^{\frac{3}{2}} - 3^{x} + 3 x^{3} d x

\frac{2}{5} x^{\frac{5}{2}} - \frac{3 ^{x}}{ln ( 3 )} + \frac{3 x ^{4}}{4} + C

Solution steps

\int x^{\frac{3}{2}} - 3^{x} + 3 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 x^{\frac{3}{2}} d x - \int 3^{x} d x + \int 3 x^{3} d x

\int x^{\frac{3}{2}} d x = \frac{2}{5} x^{\frac{5}{2}}

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

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

= \frac{2}{5} x^{\frac{5}{2}} - \frac{3 ^{x}}{ln ( 3 )} + \frac{3 x ^{4}}{4}

Add a constant to the solution

= \frac{2}{5} x^{\frac{5}{2}} - \frac{3 ^{x}}{ln ( 3 )} + \frac{3 x ^{4}}{4} + C

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