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

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

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integral of sin(x)*e^{cos(x)}

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

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

Solution steps

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

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 (x)

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

Add a constant to the solution

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

\frac{d}{d x} (\frac{30}{x ^{4}})

y = x^{2} (4 x^{4} + 5 x^{3} - 16)

\frac{\partial}{\partial y} (1 + x^{3} + y^{3})

\int_{1}^{4} \frac{2}{x ^{3}} d x

f (x) = 5 cot (\frac{x}{8})

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