Solve = ∫ 6.67*10^-11*6*10^24/6378000+1000000

$$= \int \frac { 6.67 \cdot 10 ^ { - 11 } \cdot 6 \cdot 10 ^ { 24 } } { 6378000 + 1000000 }$$

Evaluate

$$\frac{200100000000x}{3689}+С$$

Solution Steps

To multiply powers of the same base, add their exponents. Add -11 and 24 to get 13.

$$\int \frac{6.67\times 10^{13}\times 6}{6378000+1000000}\mathrm{d}x$$

Calculate 10 to the power of 13 and get 10000000000000.

$$\int \frac{6.67\times 10000000000000\times 6}{6378000+1000000}\mathrm{d}x$$

Multiply 6.67 and 10000000000000 to get 66700000000000.

$$\int \frac{66700000000000\times 6}{6378000+1000000}\mathrm{d}x$$

Multiply 66700000000000 and 6 to get 400200000000000.

$$\int \frac{400200000000000}{6378000+1000000}\mathrm{d}x$$

Add 6378000 and 1000000 to get 7378000.

$$\int \frac{400200000000000}{7378000}\mathrm{d}x$$

Reduce the fraction \frac{400200000000000}{7378000} to lowest terms by extracting and canceling out 2000.

$$\int \frac{200100000000}{3689}\mathrm{d}x$$

Find the integral of \frac{200100000000}{3689} using the table of common integrals rule \int a\mathrm{d}x=ax.

$$\frac{200100000000x}{3689}$$

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.

$$\frac{200100000000x}{3689}+С$$

Differentiate w.r.t. x

$$\frac{200100000000}{3689} = 54242342\frac{362}{3689} = 54242342.09812958$$