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Popular >

integral of (5x-x^2)

Solution

\int (5 x - x^{2}) d x

Solution

\frac{5 x ^{2}}{2} - \frac{x ^{3}}{3} + C

Solution steps

\int 5 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 5 x d x - \int x^{2} d x

\int 5 x d x = \frac{5 x ^{2}}{2}

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

= \frac{5 x ^{2}}{2} - \frac{x ^{3}}{3}

Add a constant to the solution

= \frac{5 x ^{2}}{2} - \frac{x ^{3}}{3} + C

Popular Examples

integral of x/(\sqrt[3]{x)}

integral of 10x^5e^x

\int 10 x^{5} e^{x} d x

7(dy)/(dx)=(e^ysin^2(x))/(ysec(x))

7 \frac{d y}{d x} = \frac{e ^{y} sin ^{2} ( x )}{y sec ( x )}

f^{'} (t)

limit as x approaches 0+of 1-x

x \to 0 + lim (1 - x)

Frequently Asked Questions (FAQ)

What is the integral of (5x-x^2) ?
The integral of (5x-x^2) is (5x^2)/2-(x^3)/3+C