What is the integral of e^{cos(x)}sin(x) ?

The integral of e^{cos(x)}sin(x) is -e^{cos(x)}+C

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integral of e^{cos(x)}sin(x)

\int e^{c o s (x)} sin (x) d x

- e^{c o s (x)} + C

Solution steps

\int e^{c o s (x)} sin (x) d x

Apply u-substitution

: \int - e^{u} d u

= \int - e^{u} d u

Take the constant out:

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

= - \int e^{u} d u

Use the common integral:

\int e^{u} d u = e^{u}

= - e^{u}

Substitute back

u = cos (x)

= - e^{c o s (x)}

Add a constant to the solution

= - e^{c o s (x)} + C

\frac{\partial}{\partial x} (- 2 sin (x))

y^{^{''}} - 2 y^{^{'}} - 3 y = 0, y (0) = 2, y^{^{'}} (0) = 2

(y + 4) y^{^{'}} = 2 x y + 4 y

\frac{1}{X - 1}, 12

\frac{d}{d x} (2 x^{3} - 2 x)

What is the integral of e^{cos(x)}sin(x) ?
The integral of e^{cos(x)}sin(x) is -e^{cos(x)}+C