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Popular Calculus >

integral of 1/(xy^2)

Solution

\int \frac{1}{x y ^{2}} d y

Solution

- \frac{1}{x y} + C

Solution steps

\int \frac{1}{x y ^{2}} d y

Take the constant out:

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

= \frac{1}{x} \cdot \int \frac{1}{y ^{2}} d y

Apply the Power Rule

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

Simplify

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

= - \frac{1}{x y}

Add a constant to the solution

= - \frac{1}{x y} + C

Graph

Popular Examples

integral of 5/(yln(y))+xsin(y)+x

\int \frac{5}{y ln ( y )} + x sin (y) + x d y

integral of (x+2)/(x(x^2-4x+5)^2)

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

integral of (x+1)7^{(x+1)^2}

\int (x + 1) 7^{(x + 1)^{2}} d x

integral of 3x^2+3x

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

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

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

Frequently Asked Questions (FAQ)

What is the integral of 1/(xy^2) ?
The integral of 1/(xy^2) is -1/(xy)+C