What is the integral of e^{cos(9t)}sin(9t) ?

The integral of e^{cos(9t)}sin(9t) is -1/9 e^{cos(9t)}+C

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integral of e^{cos(9t)}sin(9t)

\int e^{c o s (9 t)} sin (9 t) d t

- \frac{1}{9} e^{c o s (9 t)} + C

Solution steps

\int e^{c o s (9 t)} sin (9 t) d t

Apply u-substitution

: \int e^{c o s (u)} sin (u) \frac{1}{9} d u

= \int e^{c o s (u)} sin (u) \frac{1}{9} d u

Take the constant out:

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

= \frac{1}{9} \cdot \int e^{c o s (u)} sin (u) d u

Apply u-substitution

: \int - e^{v} d v

= \frac{1}{9} \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}{9} (- \int e^{v} d v)

Use the common integral:

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

= \frac{1}{9} (- e^{v})

Substitute back

= \frac{1}{9} (- e^{c o s (9 t)})

Simplify

= - \frac{1}{9} e^{c o s (9 t)}

Add a constant to the solution

= - \frac{1}{9} e^{c o s (9 t)} + C

\int 6 + x^{2} d x

x \to - 1 lim (x + 1)

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

f (x) = \frac{2 x + x ^{2}}{( 1 + x ) ^{2}}

\frac{\partial}{\partial x} (\frac{Y ( x )}{x})

What is the integral of e^{cos(9t)}sin(9t) ?
The integral of e^{cos(9t)}sin(9t) is -1/9 e^{cos(9t)}+C