Evaluate the Integral integral of (10+0.01x-0.001x^2) with respect to x

$\int (10 + 0.01 x - 0.001 x^{2}) d x$

Remove parentheses.

$\int 10 + 0.01 x - 0.001 x^{2} d x$

Split the single integral into multiple integrals.

$\int 10 d x + \int 0.01 x d x + \int - 0.001 x^{2} d x$

Apply the constant rule.

$10 x + C + \int 0.01 x d x + \int - 0.001 x^{2} d x$

Since $0.01$ is constant with respect to $x$ , move $0.01$ out of the integral.

$10 x + C + 0.01 \int x d x + \int - 0.001 x^{2} d x$

By the Power Rule, the integral of $x$ with respect to $x$ is $\frac{1}{2} x^{2}$ .

$10 x + C + 0.01 (\frac{1}{2} x^{2} + C) + \int - 0.001 x^{2} d x$

Since $- 0.001$ is constant with respect to $x$ , move $- 0.001$ out of the integral.

$10 x + C + 0.01 (\frac{1}{2} x^{2} + C) - 0.001 \int x^{2} d x$

By the Power Rule, the integral of $x^{2}$ with respect to $x$ is $\frac{1}{3} x^{3}$ .

$10 x + C + 0.01 (\frac{1}{2} x^{2} + C) - 0.001 (\frac{1}{3} x^{3} + C)$

Simplify.

$10 x + \frac{x^{2}}{200} - 0.001 (\frac{1}{3} x^{3}) + C$

Simplify.

Combine $\frac{1}{3}$ and $x^{3}$ .

$10 x + \frac{x^{2}}{200} - 0.001 \frac{x^{3}}{3} + C$

Combine $- 0.001$ and $\frac{x^{3}}{3}$ .

$10 x + \frac{x^{2}}{200} + \frac{- 0.001 x^{3}}{3} + C$

Move the negative in front of the fraction.

$10 x + \frac{x^{2}}{200} - \frac{0.001 x^{3}}{3} + C$

Reorder terms.

$10 x + \frac{1}{200} x^{2} - \frac{0.001}{3} x^{3} + C$