What is the integral of (5x^3-4sqrt(x)) ?

The integral of (5x^3-4sqrt(x)) is (5x^4)/4-8/3 x^{3/2}+C

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integral of (5x^3-4sqrt(x))

\int (5 x^{3} - 4 x) d x

\frac{5 x ^{4}}{4} - \frac{8}{3} x^{\frac{3}{2}} + C

Solution steps

\int 5 x^{3} - 4 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 5 x^{3} d x - \int 4 x d x

\int 5 x^{3} d x = \frac{5 x ^{4}}{4}

\int 4 x d x = \frac{8}{3} x^{\frac{3}{2}}

= \frac{5 x ^{4}}{4} - \frac{8}{3} x^{\frac{3}{2}}

Add a constant to the solution

= \frac{5 x ^{4}}{4} - \frac{8}{3} x^{\frac{3}{2}} + C

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What is the integral of (5x^3-4sqrt(x)) ?
The integral of (5x^3-4sqrt(x)) is (5x^4)/4-8/3 x^{3/2}+C