What is the integral of (1/(6x^3)) ?

The integral of (1/(6x^3)) is -1/(12x^2)+C

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integral of (1/(6x^3))

\int (\frac{1}{6 x ^{3}}) d x

- \frac{1}{12 x ^{2}} + C

Solution steps

\int \frac{1}{6 x ^{3}} d x

Take the constant out:

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

= \frac{1}{6} \cdot \int \frac{1}{x ^{3}} d x

Apply the Power Rule

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

= \frac{1}{6} (- \frac{1}{2 x ^{2}})

Simplify

\frac{1}{6} (- \frac{1}{2 x ^{2}}) : - \frac{1}{12 x ^{2}}

= - \frac{1}{12 x ^{2}}

Add a constant to the solution

= - \frac{1}{12 x ^{2}} + C

\frac{d}{d x} ((x - 4) \cdot ln (\frac{x}{4}))

\int \frac{e ^{- \frac{1}{x}}}{x ^{2}} d x

\frac{d x}{d t} = x (100 - x)

\int e^{- \frac{x}{4}} d x

y = \frac{6 x}{x + 5}, (- 3, - 9)