What is the integral of 3e^{cos(x)}sin(x) ?

The integral of 3e^{cos(x)}sin(x) is -3e^{cos(x)}+C

Popular >

integral of 3e^{cos(x)}sin(x)

\int 3 e^{c o s (x)} sin (x) d x

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

Solution steps

\int 3 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

= 3 \cdot \int e^{c o s (x)} sin (x) d x

Apply u-substitution

: \int - e^{u} d u

= 3 \cdot \int - e^{u} d u

Take the constant out:

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

= 3 (- \int e^{u} d u)

Use the common integral:

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

= 3 (- e^{u})

Substitute back

u = cos (x)

= 3 (- e^{c o s (x)})

Simplify

= - 3 e^{c o s (x)}

Add a constant to the solution

= - 3 e^{c o s (x)} + C

\int 12 x^{2} - 6 x + \frac{4}{x} d x

\int \frac{1 + x ^{2}}{1 + x ^{2}} d x

\int \frac{1}{x ^{3} ( 1 + x ^{2} )} d x

\int 30 x^{4} d x

\int (4 - 2 x) d x

What is the integral of 3e^{cos(x)}sin(x) ?
The integral of 3e^{cos(x)}sin(x) is -3e^{cos(x)}+C