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Popular >

integral of 5x^{-2}

Solution

\int 5 x^{- 2} d x

Solution

- \frac{5}{x} + C

Solution steps

\int 5 x^{- 2} d x

Take the constant out:

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

= 5 \cdot \int x^{- 2} d x

Apply the Power Rule

: - \frac{1}{x}

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

Simplify

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

= - \frac{5}{x}

Add a constant to the solution

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

Graph

Popular Examples

integral of 5x^6

\int 5 x^{6} d x

derivative of arctan((sqrt(1+x^2)-1/x))

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

integral of x^2(5x^3-4)^4

\int x^{2} (5 x^{3} - 4)^{4} d x

(dy)/(dx)=y^2-(xy)^2

\frac{d y}{d x} = y^{2} - (x y)^{2}

derivative of-2x^5+6x^4-4x^3-4x^2+6x-2

\frac{d}{d x} (- 2 x^{5} + 6 x^{4} - 4 x^{3} - 4 x^{2} + 6 x - 2)

Frequently Asked Questions (FAQ)

What is the integral of 5x^{-2} ?
The integral of 5x^{-2} is -5/x+C