What is the integral of (sin(2θ))/(sqrt(cos(2θ))) ?

The integral of (sin(2θ))/(sqrt(cos(2θ))) is -sqrt(cos(2θ))+C

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integral of (sin(2θ))/(sqrt(cos(2θ)))

\int \frac{sin ( 2 θ )}{cos ( 2 θ )} d θ

- cos (2 θ) + C

Solution steps

\int \frac{sin ( 2 θ )}{cos ( 2 θ )} d θ

Apply u-substitution

: \int \frac{sin ( u )}{2 cos ( u )} d u

= \int \frac{sin ( u )}{2 cos ( u )} d u

Take the constant out:

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

= \frac{1}{2} \cdot \int \frac{sin ( u )}{cos ( u )} d u

Apply u-substitution

: \int - \frac{1}{v} d v

= \frac{1}{2} \cdot \int - \frac{1}{v} d v

Take the constant out:

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

= \frac{1}{2} (- \int \frac{1}{v} d v)

Apply the Power Rule

: 2 v^{\frac{1}{2}}

= \frac{1}{2} (- 2 v^{\frac{1}{2}})

Substitute back

= \frac{1}{2} (- 2 cos^{\frac{1}{2}} (2 θ))

Simplify

\frac{1}{2} (- 2 cos^{\frac{1}{2}} (2 θ)) : - cos (2 θ)

= - cos (2 θ)

Add a constant to the solution

= - cos (2 θ) + C

\frac{d}{d x} (y \cdot sin (x))

x \to 2 - lim (x - 2)

- \frac{1}{x}

- x^{2} - x + 3

y^{^{''}} - 12 y^{^{'}} + 85 y = 0

What is the integral of (sin(2θ))/(sqrt(cos(2θ))) ?
The integral of (sin(2θ))/(sqrt(cos(2θ))) is -sqrt(cos(2θ))+C