What is the integral of (sin(x)y) ?

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

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integral of (sin(x)y)

\int (sin (x) y) d y

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

Solution steps

\int sin (x) y d y

Take the constant out:

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

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

Apply the Power Rule

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

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

Simplify

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

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

Add a constant to the solution

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

\frac{d}{d x} (5 e^{- 3 x})

\int \frac{1}{4 e ^{- 5 x} + e ^{5 x}} d x

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

\frac{s}{( s + 3 ) ^{2}}

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

What is the integral of (sin(x)y) ?
The integral of (sin(x)y) is 1/2 y^2sin(x)+C