What is the integral of 8r^2-2r^4 ?

The integral of 8r^2-2r^4 is (8r^3)/3-(2r^5)/5+C

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integral of 8r^2-2r^4

\int 8 r^{2} - 2 r^{4} d r

\frac{8 r ^{3}}{3} - \frac{2 r ^{5}}{5} + C

Solution steps

\int 8 r^{2} - 2 r^{4} 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 8 r^{2} d r - \int 2 r^{4} d r

\int 8 r^{2} d r = \frac{8 r ^{3}}{3}

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

= \frac{8 r ^{3}}{3} - \frac{2 r ^{5}}{5}

Add a constant to the solution

= \frac{8 r ^{3}}{3} - \frac{2 r ^{5}}{5} + C

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What is the integral of 8r^2-2r^4 ?
The integral of 8r^2-2r^4 is (8r^3)/3-(2r^5)/5+C