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

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

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

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

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

Solution steps

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

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 (t)

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

Add a constant to the solution

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

\frac{d}{d x} (x^{l o g_{2} (x)})

\int \frac{1}{x ^{2} \cdot x ^{2} - 4} d x

x \to 0 + lim (x^{12} ln (x))

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

f (x) = 4 x^{4} + 3 x^{2} - 1

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