Solve ∫ (+5/42)+(-3/21)+(+4/28)+(-2/63)=

$$\int ( + \frac { 5 } { 42 } ) + ( - \frac { 3 } { 21 } ) + ( + \frac { 4 } { 28 } ) + ( - \frac { 2 } { 63 } ) =$$

Evaluate

$$\frac{11x}{126}+С$$

Solution Steps

Reduce the fraction \frac{3}{21} to lowest terms by extracting and canceling out 3.

$$\int \frac{5}{42}-\frac{1}{7}+\frac{4}{28}-\frac{2}{63}\mathrm{d}x$$

Least common multiple of 42 and 7 is 42. Convert \frac{5}{42} and \frac{1}{7} to fractions with denominator 42.

$$\int \frac{5}{42}-\frac{6}{42}+\frac{4}{28}-\frac{2}{63}\mathrm{d}x$$

Since \frac{5}{42} and \frac{6}{42} have the same denominator, subtract them by subtracting their numerators.

$$\int \frac{5-6}{42}+\frac{4}{28}-\frac{2}{63}\mathrm{d}x$$

Subtract 6 from 5 to get -1.

$$\int -\frac{1}{42}+\frac{4}{28}-\frac{2}{63}\mathrm{d}x$$

Reduce the fraction \frac{4}{28} to lowest terms by extracting and canceling out 4.

$$\int -\frac{1}{42}+\frac{1}{7}-\frac{2}{63}\mathrm{d}x$$

Least common multiple of 42 and 7 is 42. Convert -\frac{1}{42} and \frac{1}{7} to fractions with denominator 42.

$$\int -\frac{1}{42}+\frac{6}{42}-\frac{2}{63}\mathrm{d}x$$

Since -\frac{1}{42} and \frac{6}{42} have the same denominator, add them by adding their numerators.

$$\int \frac{-1+6}{42}-\frac{2}{63}\mathrm{d}x$$

Add -1 and 6 to get 5.

$$\int \frac{5}{42}-\frac{2}{63}\mathrm{d}x$$

Least common multiple of 42 and 63 is 126. Convert \frac{5}{42} and \frac{2}{63} to fractions with denominator 126.

$$\int \frac{15}{126}-\frac{4}{126}\mathrm{d}x$$

Since \frac{15}{126} and \frac{4}{126} have the same denominator, subtract them by subtracting their numerators.

$$\int \frac{15-4}{126}\mathrm{d}x$$

Subtract 4 from 15 to get 11.

$$\int \frac{11}{126}\mathrm{d}x$$

Find the integral of \frac{11}{126} using the table of common integrals rule \int a\mathrm{d}x=ax.

$$\frac{11x}{126}$$

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.

$$\frac{11x}{126}+С$$

Differentiate w.r.t. x

$$\frac{11}{126} = 0.0873015873015873$$