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Popular >

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 (sin^2(x))/(cos^5(x))

\int \frac{sin ^{2} ( x )}{cos ^{5} ( x )} d x

integral of (x^7)/(1+x^4)

\int \frac{x ^{7}}{1 + x ^{4}} d x

integral of (sqrt(1-(ln(x))^2))/(xln(x))

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

integral of x(2x+1)sqrt(2x+1)

\int x (2 x + 1) 2 x + 1 d x

integral of (x^2+3x-12)/(x^3+3x^2-28x)

\int \frac{x ^{2} + 3 x - 12}{x ^{3} + 3 x ^{2} - 28 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