What is the integral of 3sqrt(sin(v))cos(v) ?

The integral of 3sqrt(sin(v))cos(v) is 2sin^{3/2}(v)+C

integral of 3sqrt(sin(v))cos(v)

\int 3 sin (v) cos (v) d v

2 sin^{\frac{3}{2}} (v) + C

Solution steps

\int 3 sin (v) cos (v) d v

Take the constant out:

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

= 3 \cdot \int sin (v) cos (v) d v

Apply u-substitution

= 3 \cdot \int u d u

Apply the Power Rule

= 3 \cdot \frac{2}{3} u^{\frac{3}{2}}

Substitute back

u = sin (v)

= 3 \cdot \frac{2}{3} sin^{\frac{3}{2}} (v)

Simplify

3 \cdot \frac{2}{3} sin^{\frac{3}{2}} (v) : 2 sin^{\frac{3}{2}} (v)

= 2 sin^{\frac{3}{2}} (v)

Add a constant to the solution

= 2 sin^{\frac{3}{2}} (v) + C

\int e^{- 2 x} \cdot sin (\frac{x}{2}) d x

\int 400 e^{- 0.1 x} d x

\int 2 csc (x) cot (x) - sec (x) tan (x) d x

\int \frac{e ^{x^{- 3}}}{x ^{4}} d x

\int 2 t sin (2 t) d t

What is the integral of 3sqrt(sin(v))cos(v) ?
The integral of 3sqrt(sin(v))cos(v) is 2sin^{3/2}(v)+C