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

The integral of (Inx)/(x^3) is -(In)/x+C

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integral of (Inx)/(x^3)

\int \frac{I n x}{x ^{3}} d x

- \frac{I n}{x} + C

Solution steps

\int \frac{I n x}{x ^{3}} d x

Take the constant out:

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

= I n \cdot \int \frac{x}{x ^{3}} d x

Cancel the common factor:

x

= I n \cdot \int \frac{1}{x ^{2}} d x

Apply the Power Rule

: - \frac{1}{x}

= I n (- \frac{1}{x})

Simplify

I n (- \frac{1}{x}) : - \frac{I n}{x}

= - \frac{I n}{x}

Add a constant to the solution

= - \frac{I n}{x} + C

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