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

The integral of (2x)/(x^3) is -2/x+C

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

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

- \frac{2}{x} + C

Solution steps

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

Take the constant out:

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

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

Cancel the common factor:

x

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

Apply the Power Rule

: - \frac{1}{x}

= 2 (- \frac{1}{x})

Simplify

2 (- \frac{1}{x}) : - \frac{2}{x}

= - \frac{2}{x}

Add a constant to the solution

= - \frac{2}{x} + C

\int_{- \frac{1}{2}}^{\frac{3}{2}} x - cos (π x) d x

\int sin (x) cos (\frac{1}{2} x) d x

\frac{d y}{d x} = (- y)

\frac{d}{d x} ((2 - x) (x + 1)^{2})

x \to 0 lim (x - 1)