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Popular >

integral of 2-x^2-x

Solution

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

Solution

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

Solution steps

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

\int 2 d x = 2 x

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

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

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

Add a constant to the solution

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

Popular Examples

integral of (10000-5000x)/((x^2-4x+5)^2)

\int \frac{10000 - 5000 x}{( x ^{2} - 4 x + 5 ) ^{2}} d x

sum from n=0 to infinity of (n!)/(104^n)

n = 0 \sum \infty \frac{n !}{10 4 ^{n}}

derivative of f(x)=((1))/((1+x^2))derivative of

f (x) = \frac{( 1 )}{( 1 + x ^{2} )}

integral of (e^tcos(e^t))/(3+3sin(e^t))

\int \frac{e ^{t} cos ( e ^{t} )}{3 + 3 sin ( e ^{t} )} d t

limit as x approaches+(-11) of x^2+11

x \to + (- 11) lim (x^{2} + 11)

Frequently Asked Questions (FAQ)

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