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

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

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

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

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

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

x \to - 5 lim (\frac{∣ x + 5 ∣}{x + 5})

y = \frac{4}{x}, y = \frac{4}{x ^{2}}, x = 5

\int 1 + \frac{1}{x} d x

\frac{d}{d x} (6 e^{5 x} + e^{- x^{2}})

x^{2}, 4 x - x^{2}

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