What is the integral of x-(e^x)/(y^2)-2y ?

The integral of x-(e^x)/(y^2)-2y is (e^x)/y+xy-y^2+C

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integral of x-(e^x)/(y^2)-2y

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

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

Solution steps

\int x - \frac{e ^{x}}{y ^{2}} - 2 y 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 \frac{e ^{x}}{y ^{2}} d y + \int x d y - \int 2 y d y

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

\int x d y = x y

\int 2 y d y = y^{2}

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

Simplify

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

Add a constant to the solution

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

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