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

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

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integral of (sqrt(x)-2)x^2

\int (x - 2) x^{2} d x

\frac{2}{7} x^{\frac{7}{2}} - \frac{2 x ^{3}}{3} + C

Solution steps

\int (x - 2) x^{2} d x

Expand

(x - 2) x^{2} : x^{\frac{5}{2}} - 2 x^{2}

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

\int x^{\frac{5}{2}} d x = \frac{2}{7} x^{\frac{7}{2}}

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

= \frac{2}{7} x^{\frac{7}{2}} - \frac{2 x ^{3}}{3}

Add a constant to the solution

= \frac{2}{7} x^{\frac{7}{2}} - \frac{2 x ^{3}}{3} + C

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