Solve ∫ 2*1,9*10^-18-2*6,62*10^-32*6*10^14/9,1*10^-31

$$\int \frac { 2 \cdot 1,9 \cdot 10 ^ { - 18 } - 2 \cdot 6,62 \cdot 10 ^ { - 32 } \cdot 6 \cdot 10 ^ { 14 } } { 9,1 \cdot 10 ^ { - 31 } }$$

Evaluate

$$-\frac{7564000000000000x}{91}+С$$

Solution Steps

To multiply powers of the same base, add their exponents. Add -32 and 14 to get -18.

$$\int \frac{2\times 1.9\times 10^{-18}-2\times 6.62\times 10^{-18}\times 6}{9.1\times 10^{-31}}\mathrm{d}x$$

Multiply 2 and 1.9 to get 3.8.

$$\int \frac{3.8\times 10^{-18}-2\times 6.62\times 10^{-18}\times 6}{9.1\times 10^{-31}}\mathrm{d}x$$

Calculate 10 to the power of -18 and get \frac{1}{1000000000000000000}.

$$\int \frac{3.8\times \frac{1}{1000000000000000000}-2\times 6.62\times 10^{-18}\times 6}{9.1\times 10^{-31}}\mathrm{d}x$$

Multiply 3.8 and \frac{1}{1000000000000000000} to get \frac{19}{5000000000000000000}.

$$\int \frac{\frac{19}{5000000000000000000}-2\times 6.62\times 10^{-18}\times 6}{9.1\times 10^{-31}}\mathrm{d}x$$

Multiply 2 and 6.62 to get 13.24.

$$\int \frac{\frac{19}{5000000000000000000}-13.24\times 10^{-18}\times 6}{9.1\times 10^{-31}}\mathrm{d}x$$

Calculate 10 to the power of -18 and get \frac{1}{1000000000000000000}.

$$\int \frac{\frac{19}{5000000000000000000}-13.24\times \frac{1}{1000000000000000000}\times 6}{9.1\times 10^{-31}}\mathrm{d}x$$

Multiply 13.24 and \frac{1}{1000000000000000000} to get \frac{331}{25000000000000000000}.

$$\int \frac{\frac{19}{5000000000000000000}-\frac{331}{25000000000000000000}\times 6}{9.1\times 10^{-31}}\mathrm{d}x$$

Multiply \frac{331}{25000000000000000000} and 6 to get \frac{993}{12500000000000000000}.

$$\int \frac{\frac{19}{5000000000000000000}-\frac{993}{12500000000000000000}}{9.1\times 10^{-31}}\mathrm{d}x$$

Subtract \frac{993}{12500000000000000000} from \frac{19}{5000000000000000000} to get -\frac{1891}{25000000000000000000}.

$$\int \frac{-\frac{1891}{25000000000000000000}}{9.1\times 10^{-31}}\mathrm{d}x$$

Calculate 10 to the power of -31 and get \frac{1}{10000000000000000000000000000000}.

$$\int \frac{-\frac{1891}{25000000000000000000}}{9.1\times \frac{1}{10000000000000000000000000000000}}\mathrm{d}x$$

Multiply 9.1 and \frac{1}{10000000000000000000000000000000} to get \frac{91}{100000000000000000000000000000000}.

$$\int \frac{-\frac{1891}{25000000000000000000}}{\frac{91}{100000000000000000000000000000000}}\mathrm{d}x$$

Divide -\frac{1891}{25000000000000000000} by \frac{91}{100000000000000000000000000000000} by multiplying -\frac{1891}{25000000000000000000} by the reciprocal of \frac{91}{100000000000000000000000000000000}.

$$\int -\frac{1891}{25000000000000000000}\times \frac{100000000000000000000000000000000}{91}\mathrm{d}x$$

Multiply -\frac{1891}{25000000000000000000} and \frac{100000000000000000000000000000000}{91} to get -\frac{7564000000000000}{91}.

$$\int -\frac{7564000000000000}{91}\mathrm{d}x$$

Find the integral of -\frac{7564000000000000}{91} using the table of common integrals rule \int a\mathrm{d}x=ax.

$$-\frac{7564000000000000x}{91}$$

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.

$$-\frac{7564000000000000x}{91}+С$$

Differentiate w.r.t. x

$$-\frac{7564000000000000}{91} = -83120879120879\frac{11}{91} = -83120879120879.12$$