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Popular >

integral of x^2+2x+2

Solution

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

Solution

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

Solution steps

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

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

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

\int 2 d x = 2 x

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

Add a constant to the solution

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

Popular Examples

integral from 0 to pi/2 of sin^2(1)

\int_{0}^{\frac{π}{2}} sin^{2} (1) d x

derivative of 1-e^{-ax}

\frac{d}{d x} (1 - e^{- a x})

integral from-1 to 2 of y^3+8

\int_{- 1}^{2} y^{3} + 8 d y

integral of (1-t)e^{12t-6t^2}

\int (1 - t) e^{12 t - 6 t^{2}} d t

y^{^{'}} = y (x y^{2} + 2)

Frequently Asked Questions (FAQ)

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