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

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

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

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

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

Solution steps

\int cos (x) sin (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

- \frac{1}{( x + 2 ) ^{2}}

f (x) = cos (x^{2}) \cdot 2 x

\int \frac{15}{16 + r ^{2}} d r

6 e^{- 4 t} + 5 e^{- 5 t} + 4 t e^{- 6 t}

\frac{d}{d x} (4 (x^{2} + 5 x + 2) tan (- x))

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