What is the integral of (5x^6)/(12x^7) ?

The integral of (5x^6)/(12x^7) is 5/12 ln|x|+C

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integral of (5x^6)/(12x^7)

\int \frac{5 x ^{6}}{12 x ^{7}} d x

\frac{5}{12} ln ∣ x ∣ + C

Solution steps

\int \frac{5 x ^{6}}{12 x ^{7}} d x

Take the constant out:

\int a \cdot f (x) d x = a \cdot \int f (x) d x

= \frac{5}{12} \cdot \int \frac{x ^{6}}{x ^{7}} d x

Simplify

\frac{x ^{6}}{x ^{7}} : \frac{1}{x}

= \frac{5}{12} \cdot \int \frac{1}{x} d x

Use the common integral:

\int \frac{1}{x} d x = ln (∣ x ∣)

= \frac{5}{12} ln ∣ x ∣

Add a constant to the solution

= \frac{5}{12} ln ∣ x ∣ + C

What is the integral of (5x^6)/(12x^7) ?
The integral of (5x^6)/(12x^7) is 5/12 ln|x|+C