What is the integral of (x^4+sqrt(x^3)) ?

The integral of (x^4+sqrt(x^3)) is (x^5)/5+2/5 x^{5/2}+C

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integral of (x^4+sqrt(x^3))

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

\frac{x ^{5}}{5} + \frac{2}{5} x^{\frac{5}{2}} + C

Solution steps

\int x^{4} + 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^{4} d x + \int x^{3} d x

\int x^{4} d x = \frac{x ^{5}}{5}

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

= \frac{x ^{5}}{5} + \frac{2}{5} x^{\frac{5}{2}}

Add a constant to the solution

= \frac{x ^{5}}{5} + \frac{2}{5} x^{\frac{5}{2}} + C

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