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Popular >

integral of k/(x^6)

Solution

\int \frac{k}{x ^{6}} d x

Solution

- \frac{k}{5 x ^{5}} + C

Solution steps

\int \frac{k}{x ^{6}} d x

Take the constant out:

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

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

Apply the Power Rule

: - \frac{1}{5 x ^{5}}

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

Simplify

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

= - \frac{k}{5 x ^{5}}

Add a constant to the solution

= - \frac{k}{5 x ^{5}} + C

Popular Examples

derivative of 1/3 (x^2+2^{3/2})

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

integral of-(4000x)/((1+x^2))

\int - \frac{4000 x}{( 1 + x ^{2} )} d x

integral of 3/(2+x)

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

(dy)/(dx)+10tan(10x)y=5cos(10x)

\frac{d y}{d x} + 10 tan (10 x) y = 5 cos (10 x)

y^{^{'}} = y^{2} sin (t)

Frequently Asked Questions (FAQ)

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