What is the integral of 4e^{cos(x)}sin(x) ?

The integral of 4e^{cos(x)}sin(x) is -4e^{cos(x)}+C

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integral of 4e^{cos(x)}sin(x)

\int 4 e^{c o s (x)} sin (x) d x

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

Solution steps

\int 4 e^{c o s (x)} sin (x) d x

Take the constant out:

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

= 4 \cdot \int e^{c o s (x)} sin (x) d x

Apply u-substitution

: \int - e^{u} d u

= 4 \cdot \int - e^{u} d u

Take the constant out:

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

= 4 (- \int e^{u} d u)

Use the common integral:

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

= 4 (- e^{u})

Substitute back

u = cos (x)

= 4 (- e^{c o s (x)})

Simplify

= - 4 e^{c o s (x)}

Add a constant to the solution

= - 4 e^{c o s (x)} + C

\int \frac{2 sin ( x )}{cos ( x )} d x

f (x) = tan (8 x)

\int \frac{1}{( x ^{2} + 4 ) ( x + 2 )} d x

t \to 0 lim (tan (7 t))

\frac{\partial}{\partial x} (10 x^{5} y^{4} e^{- x})

What is the integral of 4e^{cos(x)}sin(x) ?
The integral of 4e^{cos(x)}sin(x) is -4e^{cos(x)}+C