What is the integral of (2ysin(z)) ?

The integral of (2ysin(z)) is y^2sin(z)+C

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integral of (2ysin(z))

\int (2 y sin (z)) d y

y^{2} sin (z) + C

Solution steps

\int 2 y sin (z) d y

Take the constant out:

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

= 2 sin (z) \cdot \int y d y

Apply the Power Rule

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

= 2 sin (z) \frac{y ^{2}}{2}

Simplify

2 sin (z) \frac{y ^{2}}{2} : y^{2} sin (z)

= y^{2} sin (z)

Add a constant to the solution

= y^{2} sin (z) + C

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