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

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

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

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

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

Solution steps

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

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 (z)

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

Add a constant to the solution

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

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