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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

Popular Examples

(2x-1)dx+(7y+5)dy=0

(2 x - 1) d x + (7 y + 5) d y = 0

derivative of 2e^{x-1}

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

(\partial)/(\partial x)(2y-2x)

\frac{\partial}{\partial x} (2 y - 2 x)

integral from-1 to 0 of 3e^{-3x}

\int_{- 1}^{0} 3 e^{- 3 x} d x

tangent of f(x)=(1+2x)/(1-2x)enel,(1,-3)tangent of

f (x) = \frac{1 + 2 x}{1 - 2 x} e n e l, (1, - 3)

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