Solve ∫ (frac{60*1*6*10^{19}*6*10^{2}}{9*1*10^-31*2*10^7})^2+4*10^14

$$\int ( \frac { 60 \times 1 \cdot 6 \times 10 ^ { 19 } \times 6 \times 10 ^ { 2 } } { 9 \cdot 1 \times 10 ^ { - 31 } \times 2 \times 10 ^ { 7 } } ) ^ { 2 } + 4 \times 10 ^ { 14 }$$

Evaluate

$$14400000000000000000000000000000000000000000000000000000000000000000000000000000400000000000000x+С$$

Solution Steps

To multiply powers of the same base, add their exponents. Add 19 and 2 to get 21.

$$\int \left(\frac{60\times 1\times 6\times 10^{21}\times 6}{9\times 1\times 10^{-31}\times 2\times 10^{7}}\right)^{2}+4\times 10^{14}\mathrm{d}x$$

To multiply powers of the same base, add their exponents. Add -31 and 7 to get -24.

$$\int \left(\frac{60\times 1\times 6\times 10^{21}\times 6}{9\times 1\times 10^{-24}\times 2}\right)^{2}+4\times 10^{14}\mathrm{d}x$$

Cancel out 2\times 3\times 3 in both numerator and denominator.

$$\int \left(\frac{2\times 6\times 10\times 10^{21}}{10^{-24}}\right)^{2}+4\times 10^{14}\mathrm{d}x$$

To divide powers of the same base, subtract the denominator's exponent from the numerator's exponent.

$$\int \left(2\times 6\times 10^{21}\times 10^{25}\right)^{2}+4\times 10^{14}\mathrm{d}x$$

Multiply 2 and 6 to get 12.

$$\int \left(12\times 10^{21}\times 10^{25}\right)^{2}+4\times 10^{14}\mathrm{d}x$$

To multiply powers of the same base, add their exponents. Add 21 and 25 to get 46.

$$\int \left(12\times 10^{46}\right)^{2}+4\times 10^{14}\mathrm{d}x$$

Expand \left(12\times 10^{46}\right)^{2}.

$$\int 12^{2}\times \left(10^{46}\right)^{2}+4\times 10^{14}\mathrm{d}x$$

To raise a power to another power, multiply the exponents. Multiply 46 and 2 to get 92.

$$\int 12^{2}\times 10^{92}+4\times 10^{14}\mathrm{d}x$$

Calculate 12 to the power of 2 and get 144.

$$\int 144\times 10^{92}+4\times 10^{14}\mathrm{d}x$$

Calculate 10 to the power of 92 and get 100000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000.

$$\int 144\times 100000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000+4\times 10^{14}\mathrm{d}x$$

Multiply 144 and 100000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000 to get 14400000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000.

$$\int 14400000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000+4\times 10^{14}\mathrm{d}x$$

Calculate 10 to the power of 14 and get 100000000000000.

$$\int 14400000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000+4\times 100000000000000\mathrm{d}x$$

Multiply 4 and 100000000000000 to get 400000000000000.

$$\int 14400000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000+400000000000000\mathrm{d}x$$

Add 14400000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000 and 400000000000000 to get 14400000000000000000000000000000000000000000000000000000000000000000000000000000400000000000000.

$$\int 14400000000000000000000000000000000000000000000000000000000000000000000000000000400000000000000\mathrm{d}x$$

Find the integral of 14400000000000000000000000000000000000000000000000000000000000000000000000000000400000000000000 using the table of common integrals rule \int a\mathrm{d}x=ax.

$$14400000000000000000000000000000000000000000000000000000000000000000000000000000400000000000000x$$

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.

$$14400000000000000000000000000000000000000000000000000000000000000000000000000000400000000000000x+С$$

Differentiate w.r.t. x

$$14400000000000000000000000000000000000000000000000000000000000000000000000000000400000000000000$$