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

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

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

\int (y - \frac{sin ^{2} ( x )}{y ^{2}}) d y

\frac{sin ^{2} ( x )}{y} + \frac{y ^{2}}{2} + C

Solution steps

\int y - \frac{sin ^{2} ( x )}{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 \frac{sin ^{2} ( x )}{y ^{2}} d y + \int y d y

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

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

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

Simplify

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

Add a constant to the solution

= \frac{sin ^{2} ( x )}{y} + \frac{y ^{2}}{2} + C

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e^{- 4 x}

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