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Popular >

integral of x^2+4x+4

Solution

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

Solution

\frac{x ^{3}}{3} + 2 x^{2} + 4 x + C

Solution steps

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

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

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

\int 4 d x = 4 x

= \frac{x ^{3}}{3} + 2 x^{2} + 4 x

Add a constant to the solution

= \frac{x ^{3}}{3} + 2 x^{2} + 4 x + C

Popular Examples

integral from 0 to 4 of-x+1

\int_{0}^{4} - x + 1 d x

limit as x approaches infinity of (sqrt(x))/(6+e^x)

x \to \infty lim (\frac{x}{6 + e ^{x}})

integral of ((4-t+t^2)/(t^2))

\int (\frac{4 - t + t ^{2}}{t ^{2}}) d t

derivative of ln(sqrt(x^2+20))

\frac{d}{d x} (ln (x^{2} + 20))

(\partial)/(\partial x)((2y)/(x^2+1))

\frac{\partial}{\partial x} (\frac{2 y}{x ^{2} + 1})

Frequently Asked Questions (FAQ)

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