Solve ∫ (3/5+1/2+7/10)div(3/4)

$$\int ( \frac { 3 } { 5 } + \frac { 1 } { 2 } + \frac { 7 } { 10 } ) \div ( \frac { 3 } { 4 } )$$

Evaluate

$$\frac{12x}{5}+С$$

Solution Steps

Least common multiple of 5 and 2 is 10. Convert \frac{3}{5} and \frac{1}{2} to fractions with denominator 10.

$$\int \frac{\frac{6}{10}+\frac{5}{10}+\frac{7}{10}}{\frac{3}{4}}\mathrm{d}x$$

Since \frac{6}{10} and \frac{5}{10} have the same denominator, add them by adding their numerators.

$$\int \frac{\frac{6+5}{10}+\frac{7}{10}}{\frac{3}{4}}\mathrm{d}x$$

Add 6 and 5 to get 11.

$$\int \frac{\frac{11}{10}+\frac{7}{10}}{\frac{3}{4}}\mathrm{d}x$$

Since \frac{11}{10} and \frac{7}{10} have the same denominator, add them by adding their numerators.

$$\int \frac{\frac{11+7}{10}}{\frac{3}{4}}\mathrm{d}x$$

Add 11 and 7 to get 18.

$$\int \frac{\frac{18}{10}}{\frac{3}{4}}\mathrm{d}x$$

Reduce the fraction \frac{18}{10} to lowest terms by extracting and canceling out 2.

$$\int \frac{\frac{9}{5}}{\frac{3}{4}}\mathrm{d}x$$

Divide \frac{9}{5} by \frac{3}{4} by multiplying \frac{9}{5} by the reciprocal of \frac{3}{4}.

$$\int \frac{9}{5}\times \frac{4}{3}\mathrm{d}x$$

Multiply \frac{9}{5} times \frac{4}{3} by multiplying numerator times numerator and denominator times denominator.

$$\int \frac{9\times 4}{5\times 3}\mathrm{d}x$$

Do the multiplications in the fraction \frac{9\times 4}{5\times 3}.

$$\int \frac{36}{15}\mathrm{d}x$$

Reduce the fraction \frac{36}{15} to lowest terms by extracting and canceling out 3.

$$\int \frac{12}{5}\mathrm{d}x$$

Find the integral of \frac{12}{5} using the table of common integrals rule \int a\mathrm{d}x=ax.

$$\frac{12x}{5}$$

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.

$$\frac{12x}{5}+С$$

Differentiate w.r.t. x

$$\frac{12}{5} = 2\frac{2}{5} = 2.4$$