What is the integral of e^ysin(x) ?

The integral of e^ysin(x) is -e^ycos(x)+C

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integral of e^ysin(x)

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

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

Solution steps

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

Take the constant out:

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

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

Use the common integral:

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

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

Simplify

= - e^{y} cos (x)

Add a constant to the solution

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

(3, 1), (1, - 8)

- 1 - x^{2}

t \to 1 lim (sin (- π t))

\frac{d}{d x} (e^{3 x + 2 x^{2}})

h \to 0 lim (h^{2} - 3)