What is the integral of tan(x)y ?

The integral of tan(x)y is 1/2 y^2tan(x)+C

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integral of tan(x)y

\int tan (x) y d y

\frac{1}{2} y^{2} tan (x) + C

Solution steps

\int tan (x) y d y

Take the constant out:

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

= tan (x) \cdot \int y d y

Apply the Power Rule

: \frac{y ^{2}}{2}

= tan (x) \frac{y ^{2}}{2}

Simplify

tan (x) \frac{y ^{2}}{2} : \frac{1}{2} y^{2} tan (x)

= \frac{1}{2} y^{2} tan (x)

Add a constant to the solution

= \frac{1}{2} y^{2} tan (x) + C

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