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Popular >

integral of 3x^2

Solution

\int 3 x^{2} d x

Solution

x^{3} + C

Solution steps

\int 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} d x

Apply the Power Rule

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

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

Simplify

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

= x^{3}

Add a constant to the solution

= x^{3} + C

Popular Examples

integral from 0 to 8 of 2pix(x^{2/3})

\int_{0}^{8} 2 π x (x^{\frac{2}{3}}) d x

derivative of 4/3 x^3

\frac{d}{d x} (\frac{4}{3} x^{3})

integral from-3 to 0 of 4x^{1/3}

\int_{- 3}^{0} 4 x^{\frac{1}{3}} d x

integral of (x^3)/(\sqrt[5]{x^2+7)}

integral of x^3sqrt(25-x^2)

\int x^{3} 25 - x^{2} d x

Frequently Asked Questions (FAQ)

What is the integral of 3x^2 ?
The integral of 3x^2 is x^3+C