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Popular >

integral of x(x+2)

Solution

\int x (x + 2) d x

Solution

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

Solution steps

\int x (x + 2) d x

Expand

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

= \int x^{2} + 2 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

= \int x^{2} d x + \int 2 x d x

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

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

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

Add a constant to the solution

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

Popular Examples

integral from 0 to 1 of 6^{3x}

\int_{0}^{1} 6^{3 x} d x

integral of (sqrt(x^2-49))/(x^3)

\int \frac{x ^{2} - 49}{x ^{3}} d x

(\partial)/(\partial x)(4xye^x)

\frac{\partial}{\partial x} (4 x y e^{x})

limit as x approaches 2 of 3x^4+2x^2-x+1

x \to 2 lim (3 x^{4} + 2 x^{2} - x + 1)

limit as x approaches-8 of x^3

x \to - 8 lim (x^{3})

Frequently Asked Questions (FAQ)

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