What is the integral of (12)/(x^5)+1/(4x^8)+6/(7x^2) ?

The integral of (12)/(x^5)+1/(4x^8)+6/(7x^2) is -3/(x^4)-1/(28x^7)-6/(7x)+C

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integral of (12)/(x^5)+1/(4x^8)+6/(7x^2)

\int \frac{12}{x ^{5}} + \frac{1}{4 x ^{8}} + \frac{6}{7 x ^{2}} d x

- \frac{3}{x ^{4}} - \frac{1}{28 x ^{7}} - \frac{6}{7 x} + C

Solution steps

\int \frac{12}{x ^{5}} + \frac{1}{4 x ^{8}} + \frac{6}{7 x ^{2}} d x

Apply the Sum Rule:

\int f (x) \pm g (x) d x = \int f (x) d x \pm \int g (x) d x

= \int \frac{12}{x ^{5}} d x + \int \frac{1}{4 x ^{8}} d x + \int \frac{6}{7 x ^{2}} d x

\int \frac{12}{x ^{5}} d x = - \frac{3}{x ^{4}}

\int \frac{1}{4 x ^{8}} d x = - \frac{1}{28 x ^{7}}

\int \frac{6}{7 x ^{2}} d x = - \frac{6}{7 x}

= - \frac{3}{x ^{4}} - \frac{1}{28 x ^{7}} - \frac{6}{7 x}

Add a constant to the solution

= - \frac{3}{x ^{4}} - \frac{1}{28 x ^{7}} - \frac{6}{7 x} + C

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What is the integral of (12)/(x^5)+1/(4x^8)+6/(7x^2) ?
The integral of (12)/(x^5)+1/(4x^8)+6/(7x^2) is -3/(x^4)-1/(28x^7)-6/(7x)+C