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

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

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

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

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

Solution steps

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

Take the constant out:

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

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

Apply u-substitution

: \int u d u

= 3 \cdot \int u d u

Apply the Power Rule

: \frac{2}{3} u^{\frac{3}{2}}

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

Substitute back

u = sin (x)

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

Simplify

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

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

Add a constant to the solution

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

\frac{\partial}{\partial x} (3 (\frac{( 4 + z )}{5 + x})^{2})

\int x 15 x - 5 d x

\frac{1}{x} d x - \frac{1}{y} d y = 0

e^{x} - x^{5}

\frac{y}{2 ( x + y )} = \frac{d y}{d x}

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