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Popular >

integral of x^2+2x+1

Solution

\int x^{2} + 2 x + 1 d x

Solution

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

Solution steps

\int x^{2} + 2 x + 1 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 1 d x

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

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

\int 1 d x = x

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

Add a constant to the solution

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

Popular Examples

derivative of (x^2-1)/(2x-3)derivative of

\frac{x ^{2} - 1}{2 x - 3}

integral from 0 to 1 of (2y)/(e^{2y)}

\int_{0}^{1} \frac{2 y}{e ^{2 y}} d y

derivative of-(x-5^2)

\frac{d}{d x} (- (x - 5)^{2})

y^{^{'}} + \frac{3}{t} y = 0

limit as x approaches 3 of x^5

x \to 3 lim (x^{5})

Frequently Asked Questions (FAQ)

What is the integral of x^2+2x+1 ?
The integral of x^2+2x+1 is (x^3)/3+x^2+x+C