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

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

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

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

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

Solution steps

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

Expand

x^{2} (x + \frac{2}{x}) : x^{3} + 2 x^{\frac{3}{2}}

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

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

\int 2 x^{\frac{3}{2}} d x = \frac{4}{5} x^{\frac{5}{2}}

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

Add a constant to the solution

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

\int \frac{x ^{7} + 3 x ^{5} - 2 x ^{3} - 4}{x ^{3}} d x

\frac{d}{d x} (\frac{e ^{1 - c o s (x)}}{cos ( x )})

\frac{d}{d u} (cos (c) (cot (u)))

y^{^{'}} = e^{2 x + y}

\int \frac{5}{5 + e ^{x}} d x

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