en

English

Español

Português

Français

Deutsch

Italiano

Русский

中文(简体)

한국어

日本語

Tiếng Việt

עברית

العربية

Popular >

integral of-5x^{-6}

Solution

\int - 5 x^{- 6} d x

Solution

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

Solution steps

\int - 5 x^{- 6} d x

Take the constant out:

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

= - 5 \cdot \int x^{- 6} d x

Apply the Power Rule

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

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

Simplify

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

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

Add a constant to the solution

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

Popular Examples

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

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

integral of 1/(x^2-x^4)

\int \frac{1}{x ^{2} - x ^{4}} d x

tangent of 5x^3-x^2y+y^3+1=0,(1,-2)tangent of

5 x^{3} - x^{2} y + y^{3} + 1 = 0, (1, - 2)

tangent of y=t^3-4t-3,(2,-3)tangent of

y = t^{3} - 4 t - 3, (2, - 3)

limit as x approaches 2+of 3/((x-2)^3)

x \to 2 + lim (\frac{3}{( x - 2 ) ^{3}})

Frequently Asked Questions (FAQ)

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