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

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

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

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

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

Solution steps

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

Apply u-substitution

: \int u d u

= \int u d u

Apply the Power Rule

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

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

Substitute back

u = sin (x)

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

Add a constant to the solution

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

y = 3 + 4 x^{2} - 2 x^{3}

\int (- cos (x)) d x

f (x) = \frac{1}{2 x + 1}

\frac{d}{d t} (5 cos (2 t))

x \to 0 lim (\frac{tan ( x )}{3 x})

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