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

The integral of x/(2x^3) is -1/(2x)+C

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integral of x/(2x^3)

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

- \frac{1}{2 x} + C

Solution steps

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

Take the constant out:

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

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

Cancel the common factor:

x

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

Apply the Power Rule

: - \frac{1}{x}

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

Simplify

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

= - \frac{1}{2 x}

Add a constant to the solution

= - \frac{1}{2 x} + C

x \to 1 lim (5 x^{5} - 8 x^{3} + 8)

\int 3 sin (4 x) + 4 sin (3 x) d x

\frac{d y}{d x} = x^{3} e^{x^{4}}

x \to 2 lim ((2 - x)^{2})

- 4 cos (2 x)