What is the integral of x^4+5sqrt(x) ?

The integral of x^4+5sqrt(x) is (x^5)/5+10/3 x^{3/2}+C

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integral of x^4+5sqrt(x)

\int x^{4} + 5 x d x

\frac{x ^{5}}{5} + \frac{10}{3} x^{\frac{3}{2}} + C

Solution steps

\int x^{4} + 5 x 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 5 x d x

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

\int 5 x d x = \frac{10}{3} x^{\frac{3}{2}}

= \frac{x ^{5}}{5} + \frac{10}{3} x^{\frac{3}{2}}

Add a constant to the solution

= \frac{x ^{5}}{5} + \frac{10}{3} x^{\frac{3}{2}} + C

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What is the integral of x^4+5sqrt(x) ?
The integral of x^4+5sqrt(x) is (x^5)/5+10/3 x^{3/2}+C