Solve ∫ (2000*1000/9.8*1000)/3.14*frac{150^2{2000^2}*3000}=

$$\int \frac { ( \frac { 2000 \times 1000 } { 9.8 \times 1000 } ) } { 3.14 \times \frac { 150 ^ { 2 } } { 2000 ^ { 2 } } \times 3000 } =$$

Evaluate

$$\frac{800000x}{207711}+С$$

Solution Steps

Cancel out 1000 in both numerator and denominator.

$$\int \frac{\frac{2\times 1000}{9.8}}{3.14\times \frac{150^{2}}{2000^{2}}\times 3000}\mathrm{d}x$$

Multiply 2 and 1000 to get 2000.

$$\int \frac{\frac{2000}{9.8}}{3.14\times \frac{150^{2}}{2000^{2}}\times 3000}\mathrm{d}x$$

Expand \frac{2000}{9.8} by multiplying both numerator and the denominator by 10.

$$\int \frac{\frac{20000}{98}}{3.14\times \frac{150^{2}}{2000^{2}}\times 3000}\mathrm{d}x$$

Reduce the fraction \frac{20000}{98} to lowest terms by extracting and canceling out 2.

$$\int \frac{\frac{10000}{49}}{3.14\times \frac{150^{2}}{2000^{2}}\times 3000}\mathrm{d}x$$

Calculate 150 to the power of 2 and get 22500.

$$\int \frac{\frac{10000}{49}}{3.14\times \frac{22500}{2000^{2}}\times 3000}\mathrm{d}x$$

Calculate 2000 to the power of 2 and get 4000000.

$$\int \frac{\frac{10000}{49}}{3.14\times \frac{22500}{4000000}\times 3000}\mathrm{d}x$$

Reduce the fraction \frac{22500}{4000000} to lowest terms by extracting and canceling out 2500.

$$\int \frac{\frac{10000}{49}}{3.14\times \frac{9}{1600}\times 3000}\mathrm{d}x$$

Convert decimal number 3.14 to fraction \frac{314}{100}. Reduce the fraction \frac{314}{100} to lowest terms by extracting and canceling out 2.

$$\int \frac{\frac{10000}{49}}{\frac{157}{50}\times \frac{9}{1600}\times 3000}\mathrm{d}x$$

Multiply \frac{157}{50} times \frac{9}{1600} by multiplying numerator times numerator and denominator times denominator.

$$\int \frac{\frac{10000}{49}}{\frac{157\times 9}{50\times 1600}\times 3000}\mathrm{d}x$$

Do the multiplications in the fraction \frac{157\times 9}{50\times 1600}.

$$\int \frac{\frac{10000}{49}}{\frac{1413}{80000}\times 3000}\mathrm{d}x$$

Express \frac{1413}{80000}\times 3000 as a single fraction.

$$\int \frac{\frac{10000}{49}}{\frac{1413\times 3000}{80000}}\mathrm{d}x$$

Multiply 1413 and 3000 to get 4239000.

$$\int \frac{\frac{10000}{49}}{\frac{4239000}{80000}}\mathrm{d}x$$

Reduce the fraction \frac{4239000}{80000} to lowest terms by extracting and canceling out 1000.

$$\int \frac{\frac{10000}{49}}{\frac{4239}{80}}\mathrm{d}x$$

Divide \frac{10000}{49} by \frac{4239}{80} by multiplying \frac{10000}{49} by the reciprocal of \frac{4239}{80}.

$$\int \frac{10000}{49}\times \frac{80}{4239}\mathrm{d}x$$

Multiply \frac{10000}{49} times \frac{80}{4239} by multiplying numerator times numerator and denominator times denominator.

$$\int \frac{10000\times 80}{49\times 4239}\mathrm{d}x$$

Do the multiplications in the fraction \frac{10000\times 80}{49\times 4239}.

$$\int \frac{800000}{207711}\mathrm{d}x$$

Find the integral of \frac{800000}{207711} using the table of common integrals rule \int a\mathrm{d}x=ax.

$$\frac{800000x}{207711}$$

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.

$$\frac{800000x}{207711}+С$$

Differentiate w.r.t. x

$$\frac{800000}{207711} = 3\frac{176867}{207711} = 3.8515052163823773$$