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Popular Calculus >

integral of 1/(3x^6)

Solution

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

Solution

- \frac{1}{15 x ^{5}} + C

Solution steps

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

Take the constant out:

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

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

Apply the Power Rule

= \frac{1}{3} (- \frac{1}{5 x ^{5}})

Simplify

\frac{1}{3} (- \frac{1}{5 x ^{5}}) : - \frac{1}{15 x ^{5}}

= - \frac{1}{15 x ^{5}}

Add a constant to the solution

= - \frac{1}{15 x ^{5}} + C

Graph

Popular Examples

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\frac{d}{d x} (ln (\frac{e ^{x}}{x}))

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\frac{d}{d x} (5 x^{6})

limit as s approaches-1 of 1/(s^2+2s+1)

s \to - 1 lim (\frac{1}{s ^{2} + 2 s + 1})

derivative of (((x+11))/((x-11)))^5

d er i v a t i v e (\frac{( x + 11 )}{( x - 11 )})^{5}

derivative of y=sqrt(x-1)

d er i v a t i v e y = x - 1

Frequently Asked Questions (FAQ)

What is the integral of 1/(3x^6) ?
The integral of 1/(3x^6) is -1/(15x^5)+C