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

The integral of x^2(2x^2+3) is (2x^5)/5+x^3+C

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

\int x^{2} (2 x^{2} + 3) d x

\frac{2 x ^{5}}{5} + x^{3} + C

Solution steps

\int x^{2} (2 x^{2} + 3) d x

Expand

x^{2} (2 x^{2} + 3) : 2 x^{4} + 3 x^{2}

= \int 2 x^{4} + 3 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 2 x^{4} d x + \int 3 x^{2} d x

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

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

= \frac{2 x ^{5}}{5} + x^{3}

Add a constant to the solution

= \frac{2 x ^{5}}{5} + x^{3} + C

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What is the integral of x^2(2x^2+3) ?
The integral of x^2(2x^2+3) is (2x^5)/5+x^3+C