What is the integral of (sin(2x))/(sqrt(sin^2(x)-3)) ?

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

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integral of (sin(2x))/(sqrt(sin^2(x)-3))

\int \frac{sin ( 2 x )}{sin ^{2} ( x ) - 3} d x

2 sin^{2} (x) - 3 + C

Solution steps

\int \frac{sin ( 2 x )}{sin ^{2} ( x ) - 3} d x

Apply u-substitution

= \int \frac{1}{u} d u

Apply the Power Rule

= 2 u^{\frac{1}{2}}

Substitute back

u = sin^{2} (x) - 3

= 2 (sin^{2} (x) - 3)^{\frac{1}{2}}

Apply radical rule:

= 2 sin^{2} (x) - 3

Add a constant to the solution

= 2 sin^{2} (x) - 3 + C

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