What is the integral of-e^xsin(y) ?

The integral of-e^xsin(y) is e^xcos(y)+C

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integral of-e^xsin(y)

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

e^{x} cos (y) + C

Solution steps

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

Take the constant out:

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

= - e^{x} \cdot \int sin (y) d y

Use the common integral:

\int sin (y) d y = - cos (y)

= - e^{x} (- cos (y))

Simplify

= e^{x} cos (y)

Add a constant to the solution

= e^{x} cos (y) + C

\frac{\partial}{\partial y} (x + 2 y + z)

\int x^{2} e^{- 1} d x

\int \frac{( x ^{2} - 4 x + 9 )}{x ^{2} - 6 x + 9} d x

(2 x + 3 y) d x + (3 x + 2) d y = 0

\frac{( 3 s + 7 )}{s ^{2} + 2 s + 4}