What is the integral of r^2(r^3-2)^2 ?

The integral of r^2(r^3-2)^2 is (r^9)/9-(2r^6)/3+(4r^3)/3+C

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integral of r^2(r^3-2)^2

\int r^{2} (r^{3} - 2)^{2} d r

\frac{r ^{9}}{9} - \frac{2 r ^{6}}{3} + \frac{4 r ^{3}}{3} + C

Solution steps

\int r^{2} (r^{3} - 2)^{2} d r

Expand

r^{2} (r^{3} - 2)^{2} : r^{8} - 4 r^{5} + 4 r^{2}

= \int r^{8} - 4 r^{5} + 4 r^{2} d r

Apply the Sum Rule:

\int f (x) \pm g (x) d x = \int f (x) d x \pm \int g (x) d x

= \int r^{8} d r - \int 4 r^{5} d r + \int 4 r^{2} d r

\int r^{8} d r = \frac{r ^{9}}{9}

\int 4 r^{5} d r = \frac{2 r ^{6}}{3}

\int 4 r^{2} d r = \frac{4 r ^{3}}{3}

= \frac{r ^{9}}{9} - \frac{2 r ^{6}}{3} + \frac{4 r ^{3}}{3}

Add a constant to the solution

= \frac{r ^{9}}{9} - \frac{2 r ^{6}}{3} + \frac{4 r ^{3}}{3} + C

H (- 5) = 2^{x}

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

\frac{d}{d x} (3500 (1 - \frac{1}{50} x)^{2})

\int (5 x + 3) d x

y ln (x) (x d y + y d x) = (x y ln (x) - y) d y

What is the integral of r^2(r^3-2)^2 ?
The integral of r^2(r^3-2)^2 is (r^9)/9-(2r^6)/3+(4r^3)/3+C