What is the integral of 6x^2(x^2+2) ?

The integral of 6x^2(x^2+2) is 6((x^5)/5+(2x^3)/3)+C

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integral of 6x^2(x^2+2)

\int 6 x^{2} (x^{2} + 2) d x

6 (\frac{x ^{5}}{5} + \frac{2 x ^{3}}{3}) + C

Solution steps

\int 6 x^{2} (x^{2} + 2) d x

Take the constant out:

\int a \cdot f (x) d x = a \cdot \int f (x) d x

= 6 \cdot \int x^{2} (x^{2} + 2) d x

Expand

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

= 6 \cdot \int x^{4} + 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

= 6 (\int x^{4} d x + \int 2 x^{2} d x)

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

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

= 6 (\frac{x ^{5}}{5} + \frac{2 x ^{3}}{3})

Add a constant to the solution

= 6 (\frac{x ^{5}}{5} + \frac{2 x ^{3}}{3}) + C

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What is the integral of 6x^2(x^2+2) ?
The integral of 6x^2(x^2+2) is 6((x^5)/5+(2x^3)/3)+C