What is the integral of (x^2)/(8x^3) ?

The integral of (x^2)/(8x^3) is 1/8 ln|x|+C

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integral of (x^2)/(8x^3)

\int \frac{x ^{2}}{8 x ^{3}} d x

\frac{1}{8} ln ∣ x ∣ + C

Solution steps

\int \frac{x ^{2}}{8 x ^{3}} d x

Take the constant out:

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

= \frac{1}{8} \cdot \int \frac{x ^{2}}{x ^{3}} d x

Simplify

\frac{x ^{2}}{x ^{3}} : \frac{1}{x}

= \frac{1}{8} \cdot \int \frac{1}{x} d x

Use the common integral:

\int \frac{1}{x} d x = ln (∣ x ∣)

= \frac{1}{8} ln ∣ x ∣

Add a constant to the solution

= \frac{1}{8} ln ∣ x ∣ + C

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What is the integral of (x^2)/(8x^3) ?
The integral of (x^2)/(8x^3) is 1/8 ln|x|+C