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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

limit as x approaches 0 of (3-3)/x

x \to 0 lim (\frac{3 - 3}{x})

sum from k=1 to infinity of (2k+1)/k

k = 1 \sum \infty \frac{2 k + 1}{k}

(x+1)y^'+y=ln(x)

(x + 1) y^{^{'}} + y = ln (x)

maclaurin (1+x)/(1-x)maclaurin

\frac{1 + x}{1 - x}

limit as x approaches 0+of (1+2x)^{1/x}

x \to 0 + lim ((1 + 2 x)^{\frac{1}{x}})

Frequently Asked Questions (FAQ)

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