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Popular >

integral of x^2+x+2

Solution

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

Solution

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

Solution steps

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

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

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

\int 2 d x = 2 x

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

Add a constant to the solution

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

Graph

Popular Examples

integral of (13t^7+t^5)/(t^{3/2)}

\int \frac{13 t ^{7} + t ^{5}}{t ^{\frac{3}{2}}} d t

limit as x approaches 0 of x^{x^2}

x \to 0 lim (x^{x^{2}})

y^{^{'}} + 0.15 y = 1

(2x^2+y)dx+(x^2y-x)dy=0

(2 x^{2} + y) d x + (x^{2} y - x) d y = 0

(dy)/(dx)=(9x)/(5y)

\frac{d y}{d x} = \frac{9 x}{5 y}

Frequently Asked Questions (FAQ)

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