What is the integral of e^{cos(11t)}sin(11t) ?

The integral of e^{cos(11t)}sin(11t) is -1/11 e^{cos(11t)}+C

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integral of e^{cos(11t)}sin(11t)

\int e^{c o s (11 t)} sin (11 t) d t

- \frac{1}{11} e^{c o s (11 t)} + C

Solution steps

\int e^{c o s (11 t)} sin (11 t) d t

Apply u-substitution

: \int e^{c o s (u)} sin (u) \frac{1}{11} d u

= \int e^{c o s (u)} sin (u) \frac{1}{11} d u

Take the constant out:

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

= \frac{1}{11} \cdot \int e^{c o s (u)} sin (u) d u

Apply u-substitution

: \int - e^{v} d v

= \frac{1}{11} \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}{11} (- \int e^{v} d v)

Use the common integral:

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

= \frac{1}{11} (- e^{v})

Substitute back

= \frac{1}{11} (- e^{c o s (11 t)})

Simplify

= - \frac{1}{11} e^{c o s (11 t)}

Add a constant to the solution

= - \frac{1}{11} e^{c o s (11 t)} + C

\frac{d}{d x} (\frac{1}{9})

\int \frac{a + b x ^{4}}{5 a x + b x ^{5}} d x

\frac{d}{d x} (ln (21 x))

g (x) = (x^{2} + 3) (x^{2} - 4 x)

- \frac{t}{4} - \frac{3}{8} sin (2 t)

What is the integral of e^{cos(11t)}sin(11t) ?
The integral of e^{cos(11t)}sin(11t) is -1/11 e^{cos(11t)}+C