What is the integral of e^{cos(7t)}sin(7t) ?

The integral of e^{cos(7t)}sin(7t) is -1/7 e^{cos(7t)}+C

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integral of e^{cos(7t)}sin(7t)

\int e^{c o s (7 t)} sin (7 t) d t

- \frac{1}{7} e^{c o s (7 t)} + C

Solution steps

\int e^{c o s (7 t)} sin (7 t) d t

Apply u-substitution

= \int e^{c o s (u)} sin (u) \frac{1}{7} d u

Take the constant out:

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

= \frac{1}{7} \cdot \int e^{c o s (u)} sin (u) d u

Apply u-substitution

= \frac{1}{7} \cdot \int - e^{v} d v

Take the constant out:

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

= \frac{1}{7} (- \int e^{v} d v)

Use the common integral:

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

= \frac{1}{7} (- e^{v})

Substitute back

= \frac{1}{7} (- e^{c o s (7 t)})

Simplify

= - \frac{1}{7} e^{c o s (7 t)}

Add a constant to the solution

= - \frac{1}{7} e^{c o s (7 t)} + C

What is the integral of e^{cos(7t)}sin(7t) ?
The integral of e^{cos(7t)}sin(7t) is -1/7 e^{cos(7t)}+C