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

The integral of (x^5-4x^3)/(sqrt(x)) is 2/11 x^{11/2}-8/7 x^{7/2}+C

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

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

\frac{2}{11} x^{\frac{11}{2}} - \frac{8}{7} x^{\frac{7}{2}} + C

Solution steps

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

Expand

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

\int \frac{x ^{5}}{x} d x = \frac{2}{11} x^{\frac{11}{2}}

\int \frac{4 x ^{3}}{x} d x = \frac{8}{7} x^{\frac{7}{2}}

= \frac{2}{11} x^{\frac{11}{2}} - \frac{8}{7} x^{\frac{7}{2}}

Add a constant to the solution

= \frac{2}{11} x^{\frac{11}{2}} - \frac{8}{7} x^{\frac{7}{2}} + C

\frac{( s + 5 )}{( s + 3 ) ( s + 7 )}

f (x) = 2 x - \frac{16}{x}

6 cos (x) + 3 sin^{2} (x)

\frac{d}{d x} (\frac{1}{2 x})

\frac{d}{d x} (2 x + x)

What is the integral of (x^5-4x^3)/(sqrt(x)) ?
The integral of (x^5-4x^3)/(sqrt(x)) is 2/11 x^{11/2}-8/7 x^{7/2}+C