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Popular >

integral of (x+2)^2

Solution

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

Solution

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

Solution steps

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

Expand

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

= \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 of 6x^3e^{x^4}

\int 6 x^{3} e^{x^{4}} d x

integral of 4x^2cos(mx)

\int 4 x^{2} cos (m x) d x

integral of sqrt(x-3)

\int x - 3 d x

integral of (7-1/(x^6))^2(1/(x^7))

\int (7 - \frac{1}{x ^{6}})^{2} (\frac{1}{x ^{7}}) d x

f (t) = e^{t} - 1

Frequently Asked Questions (FAQ)

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