Calculus Examples

$\int 1.75 + 0.16 x - 0.0015 x^{2} d x$

Step 1

Split the single integral into multiple integrals.

$\int 1.75 d x + \int 0.16 x d x + \int - 0.0015 x^{2} d x$

Step 2

Apply the constant rule.

$1.75 x + C + \int 0.16 x d x + \int - 0.0015 x^{2} d x$

Step 3

Since $0.16$ is constant with respect to $x$ , move $0.16$ out of the integral.

$1.75 x + C + 0.16 \int x d x + \int - 0.0015 x^{2} d x$

Step 4

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

$1.75 x + C + 0.16 (\frac{1}{2} x^{2} + C) + \int - 0.0015 x^{2} d x$

Step 5

Since $- 0.0015$ is constant with respect to $x$ , move $- 0.0015$ out of the integral.

$1.75 x + C + 0.16 (\frac{1}{2} x^{2} + C) - 0.0015 \int x^{2} d x$

Step 6

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

$1.75 x + C + 0.16 (\frac{1}{2} x^{2} + C) - 0.0015 (\frac{1}{3} x^{3} + C)$

Step 7

Simplify.

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Step 7.1

Simplify.

$1.75 x + \frac{2 x^{2}}{25} - 0.0015 (\frac{1}{3} x^{3}) + C$

Step 7.2

Simplify.

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Step 7.2.1

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

$1.75 x + \frac{2 x^{2}}{25} - 0.0015 \frac{x^{3}}{3} + C$

Step 7.2.2

Combine $- 0.0015$ and $\frac{x^{3}}{3}$ .

$1.75 x + \frac{2 x^{2}}{25} + \frac{- 0.0015 x^{3}}{3} + C$

Step 7.2.3

Move the negative in front of the fraction.

$1.75 x + \frac{2 x^{2}}{25} - \frac{0.0015 x^{3}}{3} + C$

Step 8

Reorder terms.

$1.75 x + \frac{2}{25} x^{2} - \frac{0.0015}{3} x^{3} + C$