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Popular >

integral of-x^2+6x

Solution

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

Solution

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

Solution steps

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

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

\int 6 x d x = 3 x^{2}

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

Add a constant to the solution

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

Popular Examples

derivative of arctan(sqrt(4x^2-1))

\frac{d}{d x} (arctan (4 x^{2} - 1))

integral of sin^3(2θ)cot(2θ)

\int sin^{3} (2 θ) cot (2 θ) d θ

limit as x approaches infinity of (\sqrt[3]{x}+5x+3)/(-2x+x^{2/3)+7}

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

f (x) = 2 x^{3} - x^{2} + 2, (1, 3)

limit as x approaches-1+of f(x)

x \to - 1 + lim (f (x))

Frequently Asked Questions (FAQ)

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