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

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

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integral of-e^xcos(y)

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

- e^{x} sin (y) + C

Solution steps

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

Use the common integral:

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

= - e^{x} sin (y)

Add a constant to the solution

= - e^{x} sin (y) + C

\frac{\partial}{\partial x} (4 x + 6 y + 2 z)

y^{^{''}} + 2 y^{^{'}} + y = e^{- t} ln (t)

\int \frac{3}{8} x^{2} d x

\frac{d y}{d x} = \frac{x + 3 y}{y - 3 x}

\int n^{x} d x