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

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

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

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

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

Solution steps

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

Take the constant out:

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

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

Expand

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

= 3 \cdot \int 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

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

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

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

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

Add a constant to the solution

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

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