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Popular >

integral of x(x+4)

Solution

\int x (x + 4) d x

Solution

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

Solution steps

\int x (x + 4) d x

Expand

x (x + 4) : x^{2} + 4 x

= \int x^{2} + 4 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 4 x d x

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

\int 4 x d x = 2 x^{2}

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

Add a constant to the solution

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

Graph

Popular Examples

integral of sqrt(x+25)

\int x + 25 d x

integral of 2/(ln(x))

\int \frac{2}{ln ( x )} d x

integral of 1/((x-1)(x-5))

\int \frac{1}{( x - 1 ) ( x - 5 )} d x

integral of s^2e^{3s}

\int s^{2} e^{3 s} d s

integral of y^2sqrt(y^3+1)

\int y^{2} y^{3} + 1 d y

Frequently Asked Questions (FAQ)

What is the integral of x(x+4) ?
The integral of x(x+4) is (x^3)/3+2x^2+C