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Popular >

integral of (-x)/y

Solution

\int \frac{- x}{y} d x

Solution

- \frac{x ^{2}}{2 y} + C

Solution steps

\int \frac{- x}{y} d x

Take the constant out:

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

= \frac{- 1}{y} \cdot \int x d x

Simplify

= (- \frac{1}{y}) \cdot \int x d x

Apply the Power Rule

: \frac{x ^{2}}{2}

= (- \frac{1}{y}) \frac{x ^{2}}{2}

Simplify

(- \frac{1}{y}) \frac{x ^{2}}{2} : - \frac{x ^{2}}{2 y}

= - \frac{x ^{2}}{2 y}

Add a constant to the solution

= - \frac{x ^{2}}{2 y} + C

Popular Examples

derivative of f(x)=9-4x derivative of

f (x) = 9 - 4 x

derivative of y=ln(1/e)derivative of

y = ln (\frac{1}{e})

slope of 3x-x^2 slope

3 x - x^{2}

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

(s^{2} + \frac{1}{s})^{\frac{3}{2}}

limit as x approaches 1+of (x+8)/(x-1)

x \to 1 + lim (\frac{x + 8}{x - 1})

Frequently Asked Questions (FAQ)

What is the integral of (-x)/y ?
The integral of (-x)/y is -(x^2)/(2y)+C