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Popular Calculus >

integral of x^2+x+6

Solution

\int x^{2} + x + 6 d x

Solution

\frac{x ^{3}}{3} + \frac{x ^{2}}{2} + 6 x + C

Solution steps

\int x^{2} + x + 6 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 6 d x

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

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

\int 6 d x = 6 x

= \frac{x ^{3}}{3} + \frac{x ^{2}}{2} + 6 x

Add a constant to the solution

= \frac{x ^{3}}{3} + \frac{x ^{2}}{2} + 6 x + C

Graph

Popular Examples

integral of (3x^2+5x)/((x-1)(x+1)^2)

\int \frac{3 x ^{2} + 5 x}{( x - 1 ) ( x + 1 ) ^{2}} d x

x^2y^{''}-3xy^'+4y=x,y(1)=0,y^'(1)=0

x^{2} y^{^{''}} - 3 x y^{^{'}} + 4 y = x, y (1) = 0, y^{^{'}} (1) = 0

sum from n=1 to infinity of n!(2x-1)^n

n = 1 \sum \infty n! (2 x - 1)^{n}

\frac{d x}{d t} = - 8

integral of (x^4+5x^3-3)/x

\int \frac{x ^{4} + 5 x ^{3} - 3}{x} d x

Frequently Asked Questions (FAQ)

What is the integral of x^2+x+6 ?
The integral of x^2+x+6 is (x^3)/3+(x^2)/2+6x+C