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

The integral of 3x(x^2+3) is 3((x^4)/4+(3x^2)/2)+C

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integral of 3x(x^2+3)

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

3 (\frac{x ^{4}}{4} + \frac{3 x ^{2}}{2}) + C

Solution steps

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

Take the constant out:

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

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

Expand

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

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

\int x^{3} d x = \frac{x ^{4}}{4}

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

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

Add a constant to the solution

= 3 (\frac{x ^{4}}{4} + \frac{3 x ^{2}}{2}) + C

f (x) = x \cdot ln (2 x + 1)

4 sin (5 X)

\int e^{2 t} cos (t) d t

\frac{d}{d x} (\frac{1}{4} x^{2})

h \to 0 lim (sin (h))

What is the integral of 3x(x^2+3) ?
The integral of 3x(x^2+3) is 3((x^4)/4+(3x^2)/2)+C