What is the integral of (x^3+2x^2)/(sqrt(x)) ?

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

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integral of (x^3+2x^2)/(sqrt(x))

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

\frac{2}{7} x^{\frac{7}{2}} + \frac{4}{5} x^{\frac{5}{2}} + C

Solution steps

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

Expand

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

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

\int \frac{2 x ^{2}}{x} d x = \frac{4}{5} x^{\frac{5}{2}}

= \frac{2}{7} x^{\frac{7}{2}} + \frac{4}{5} x^{\frac{5}{2}}

Add a constant to the solution

= \frac{2}{7} x^{\frac{7}{2}} + \frac{4}{5} x^{\frac{5}{2}} + C

\frac{d}{d x} ((1 + 3 x)^{2})

6 y^{^{''}} - 5 y^{^{'}} + y = 0

x \to 0 lim (e^{s i n (x)})

sec^{2} (x), 8 cos (x)

x \to 3 lim (c x^{2} - 4 x)

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