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

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

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

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

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

Solution steps

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

x \to - 1 lim (x - \frac{1}{ln ∣ x ∣})

\frac{d y}{d x} - 2 y = x^{2} e^{2 x}

f (x) = 4 sin^{2} (5 x + 3)

\int_{3}^{8} \frac{x}{x ^{2} + 6 x + 13} d x

(12 y^{2} t^{2} + 10 y) d y + (8 y^{3} t) d t = 0

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