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

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

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

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

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

Solution steps

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

Take the constant out:

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

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

Apply the Power Rule

: \frac{x ^{3}}{3}

= \frac{3}{2} \cdot \frac{x ^{3}}{3}

Simplify

\frac{3}{2} \cdot \frac{x ^{3}}{3} : \frac{x ^{3}}{2}

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

Add a constant to the solution

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

\frac{d}{d x} (e^{x^{2} + 6 x})

\int (5 x + 1)^{4} d x

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

f (x) = 9 - ∣ x - 4 ∣ at x

x \to 5 - lim (\frac{2}{x ^{2} - 25})