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) 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

\int \frac{x}{x ^{3} + x ^{2} + x - 3} d x

\frac{\partial}{\partial x} (7 x + y^{4} + 1)

x e^{- x + 1}

\int [cot (x) + \frac{1}{x}] d x

\int_{0}^{1} t^{4} + t^{2} d t

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