What is the integral of 3x^2y^{-2}+2xy^{-1} ?

The integral of 3x^2y^{-2}+2xy^{-1} is (x^2)/y+(x^3)/(y^2)+C

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integral of 3x^2y^{-2}+2xy^{-1}

\int 3 x^{2} y^{- 2} + 2 x y^{- 1} d x

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

Solution steps

\int 3 x^{2} y^{- 2} + 2 x y^{- 1} d x

Apply the Sum Rule:

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

= \int 2 y^{- 1} x d x + \int 3 y^{- 2} x^{2} d x

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

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

= \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 sin^{4} (\frac{1}{2} x) cos^{4} (\frac{1}{2} x) d x

f (t) = 4 cos (t)

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

y^{^{'}} = - \frac{1 + y}{1 + x + y}

\frac{d y}{d x} = 7 y (7 - y)

What is the integral of 3x^2y^{-2}+2xy^{-1} ?
The integral of 3x^2y^{-2}+2xy^{-1} is (x^2)/y+(x^3)/(y^2)+C