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Popular >

integral of 6-x-x^2

Solution

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

Solution

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

Solution steps

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

\int 6 d x = 6 x

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

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

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

Add a constant to the solution

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

Popular Examples

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

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

integral of (x+e^{x^{-1}})/(x^2)

\int \frac{x + e ^{x^{- 1}}}{x ^{2}} d x

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

\int \frac{5 x}{x ^{2} + 3} d x

integral of (sin(x))/((1+x^2))

\int \frac{sin ( x )}{( 1 + x ^{2} )} d x

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

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

Frequently Asked Questions (FAQ)

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