Solve ∫ 2/320000^3-220000^2+12(20000) wrt x

$$\int{ \frac{ 2 }{ 3 } { 20000 }^{ 3 } -2 { 20000 }^{ 2 } +12(20000) }d x$$

Evaluate

$$\frac{15997600720000x}{3}+С$$

Solution Steps

Calculate 20000 to the power of 3 and get 8000000000000.

$$\int \frac{2}{3}\times 8000000000000-2\times 20000^{2}+12\times 20000\mathrm{d}x$$

Express \frac{2}{3}\times 8000000000000 as a single fraction.

$$\int \frac{2\times 8000000000000}{3}-2\times 20000^{2}+12\times 20000\mathrm{d}x$$

Multiply 2 and 8000000000000 to get 16000000000000.

$$\int \frac{16000000000000}{3}-2\times 20000^{2}+12\times 20000\mathrm{d}x$$

Calculate 20000 to the power of 2 and get 400000000.

$$\int \frac{16000000000000}{3}-2\times 400000000+12\times 20000\mathrm{d}x$$

Multiply 2 and 400000000 to get 800000000.

$$\int \frac{16000000000000}{3}-800000000+12\times 20000\mathrm{d}x$$

Convert 800000000 to fraction \frac{2400000000}{3}.

$$\int \frac{16000000000000}{3}-\frac{2400000000}{3}+12\times 20000\mathrm{d}x$$

Since \frac{16000000000000}{3} and \frac{2400000000}{3} have the same denominator, subtract them by subtracting their numerators.

$$\int \frac{16000000000000-2400000000}{3}+12\times 20000\mathrm{d}x$$

Subtract 2400000000 from 16000000000000 to get 15997600000000.

$$\int \frac{15997600000000}{3}+12\times 20000\mathrm{d}x$$

Multiply 12 and 20000 to get 240000.

$$\int \frac{15997600000000}{3}+240000\mathrm{d}x$$

Convert 240000 to fraction \frac{720000}{3}.

$$\int \frac{15997600000000}{3}+\frac{720000}{3}\mathrm{d}x$$

Since \frac{15997600000000}{3} and \frac{720000}{3} have the same denominator, add them by adding their numerators.

$$\int \frac{15997600000000+720000}{3}\mathrm{d}x$$

Add 15997600000000 and 720000 to get 15997600720000.

$$\int \frac{15997600720000}{3}\mathrm{d}x$$

Find the integral of \frac{15997600720000}{3} using the table of common integrals rule \int a\mathrm{d}x=ax.

$$\frac{15997600720000x}{3}$$

If F\left(x\right) is an antiderivative of f\left(x\right), then the set of all antiderivatives of f\left(x\right) is given by F\left(x\right)+C. Therefore, add the constant of integration C\in \mathrm{R} to the result.

$$\frac{15997600720000x}{3}+С$$

Differentiate w.r.t. x

$$\frac{15997600720000}{3} = 5332533573333\frac{1}{3} = 5332533573333.333$$