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

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

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

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

- \frac{2}{3} cos^{\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

Take the constant out:

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

= - \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 = cos (x)

= - \frac{2}{3} cos^{\frac{3}{2}} (x)

Add a constant to the solution

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

\frac{\partial}{\partial y} (e^{x} \cdot cos (y))

ln (2 x), 1

\frac{\partial}{\partial x} (e^{x} cos (θ))

f (x) = x^{4} - 6 x^{2} - x, at x = 1, y = 6

\int_{0}^{1} x^{2} (2 (1 - x)) d x

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