What is the integral of e^{cos(38t)}sin(38t) ?

The integral of e^{cos(38t)}sin(38t) is -1/38 e^{cos(38t)}+C

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integral of e^{cos(38t)}sin(38t)

\int e^{c o s (38 t)} sin (38 t) d t

- \frac{1}{38} e^{c o s (38 t)} + C

Solution steps

\int e^{c o s (38 t)} sin (38 t) d t

Apply u-substitution

: \int e^{c o s (u)} sin (u) \frac{1}{38} d u

= \int e^{c o s (u)} sin (u) \frac{1}{38} d u

Take the constant out:

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

= \frac{1}{38} \cdot \int e^{c o s (u)} sin (u) d u

Apply u-substitution

: \int - e^{v} d v

= \frac{1}{38} \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}{38} (- \int e^{v} d v)

Use the common integral:

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

= \frac{1}{38} (- e^{v})

Substitute back

= \frac{1}{38} (- e^{c o s (38 t)})

Simplify

= - \frac{1}{38} e^{c o s (38 t)}

Add a constant to the solution

= - \frac{1}{38} e^{c o s (38 t)} + C

\frac{d}{d x} (x^{2} + 8 x + 7)

y = x, y = 2 x - 15, y = 0

5 \frac{d v}{d t} = 49.05 - 50 v

y = \frac{1}{2} x^{2} + 2 x + 3

\frac{x - 15}{x - 15}

What is the integral of e^{cos(38t)}sin(38t) ?
The integral of e^{cos(38t)}sin(38t) is -1/38 e^{cos(38t)}+C