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Popular >

integral of (5x^2)

Solution

\int (5 x^{2}) d x

Solution

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

Solution steps

\int 5 x^{2} d x

Take the constant out:

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

= 5 \cdot \int x^{2} d x

Apply the Power Rule

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

= 5 \cdot \frac{x ^{3}}{3}

Multiply fractions:

a \cdot \frac{b}{c} = \frac{a \cdot b}{c}

= \frac{5 x ^{3}}{3}

Add a constant to the solution

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

Popular Examples

integral of (tan^2(x))/(2sec(x))

\int \frac{tan ^{2} ( x )}{2 sec ( x )} d x

integral from 0 to pi of 4xcos(x)

\int_{0}^{π} 4 x cos (x) d x

derivative of 1/(in(x-1))

\frac{d}{d x} (\frac{1}{in ( x - 1 )})

(e^{(-x^2)/2})^'

(e^{\frac{- x ^{2}}{2}})^{^{'}}

integral of 3/(1-x)

\int \frac{3}{1 - x} d x

Frequently Asked Questions (FAQ)

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