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Popular >

integral of x^2+x-3

Solution

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

Solution

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

Solution steps

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

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

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

\int 3 d x = 3 x

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

Add a constant to the solution

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

Popular Examples

derivative of sin(4x+sin^2(4x))

\frac{d}{d x} (sin (4 x) + sin^{2} (4 x))

y^{''}+3y^'+2y=e^{-t},y(0)=0,y^'(0)=0

y^{^{''}} + 3 y^{^{'}} + 2 y = e^{- t}, y (0) = 0, y^{^{'}} (0) = 0

(d^2x)/(dt)+2(dx)/(dt)+x=1

\frac{d ^{2} x}{d t} + 2 \frac{d x}{d t} + x = 1

integral of sqrt(5+x^2)

\int 5 + x^{2} d x

area y=8x,y=4x^2 area

y = 8 x, y = 4 x^{2}

Frequently Asked Questions (FAQ)

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