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Popular Calculus >

integral of 1/(5x^5)

Solution

\int \frac{1}{5 x ^{5}} d x

Solution

- \frac{1}{20 x ^{4}} + C

Solution steps

\int \frac{1}{5 x ^{5}} d x

Take the constant out:

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

= \frac{1}{5} \cdot \int \frac{1}{x ^{5}} d x

Apply the Power Rule

= \frac{1}{5} (- \frac{1}{4 x ^{4}})

Simplify

\frac{1}{5} (- \frac{1}{4 x ^{4}}) : - \frac{1}{20 x ^{4}}

= - \frac{1}{20 x ^{4}}

Add a constant to the solution

= - \frac{1}{20 x ^{4}} + C

Graph

Popular Examples

integral from 0 to 8 of sqrt(64-x^2)

\int_{0}^{8} 64 - x^{2} d x

(x^2+1)((dy)/(dx))+8x(y-1)=0,y(0)=5

(x^{2} + 1) (\frac{d y}{d x}) + 8 x (y - 1) = 0, y (0) = 5

6 x + \frac{d y}{d x} = 0

derivative of 1/({f(x)})

\frac{d}{d x} (\frac{1}{f ( x )})

integral from 1 to-1 of (x-1)(3x+2)

\int_{1}^{- 1} (x - 1) (3 x + 2) d x

Frequently Asked Questions (FAQ)

What is the integral of 1/(5x^5) ?
The integral of 1/(5x^5) is -1/(20x^4)+C