What is the integral of-2x^3y^{-3}-x^2y^{-2} ?

The integral of-2x^3y^{-3}-x^2y^{-2} is (x^2)/y+(x^3)/(y^2)+C

Popular >

integral of-2x^3y^{-3}-x^2y^{-2}

\int - 2 x^{3} y^{- 3} - x^{2} y^{- 2} d y

\frac{x ^{2}}{y} + \frac{x ^{3}}{y ^{2}} + C

Solution steps

\int - 2 x^{3} y^{- 3} - x^{2} y^{- 2} d y

Apply the Sum Rule:

\int f (x) \pm g (x) d x = \int f (x) d x \pm \int g (x) d x

= - \int x^{2} y^{- 2} d y - \int 2 x^{3} y^{- 3} d y

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

\int 2 x^{3} y^{- 3} d y = - \frac{x ^{3}}{y ^{2}}

= - (- \frac{x ^{2}}{y}) - (- \frac{x ^{3}}{y ^{2}})

Simplify

= \frac{x ^{2}}{y} + \frac{x ^{3}}{y ^{2}}

Add a constant to the solution

= \frac{x ^{2}}{y} + \frac{x ^{3}}{y ^{2}} + C

\int_{0}^{1} 2 π (x + 8) (x^{2}) d x

\frac{y , ( x + y )}{( x ^{2} + y ^{2} + x y + 3 )}

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

\int \frac{x ^{2}}{x ^{2} - 6 x + 25} d x

x \to - \infty lim (e^{4 x})

What is the integral of-2x^3y^{-3}-x^2y^{-2} ?
The integral of-2x^3y^{-3}-x^2y^{-2} is (x^2)/y+(x^3)/(y^2)+C