What is the integral of (sin(2x))/(sqrt(1+sin^2(x))) ?

The integral of (sin(2x))/(sqrt(1+sin^2(x))) is 2sqrt(1+sin^2(x))+C

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integral of (sin(2x))/(sqrt(1+sin^2(x)))

\int \frac{sin ( 2 x )}{1 + sin ^{2} ( x )} d x

2 1 + sin^{2} (x) + C

Solution steps

\int \frac{sin ( 2 x )}{1 + sin ^{2} ( x )} d x

Apply u-substitution

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

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

Apply the Power Rule

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

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

Substitute back

u = 1 + sin^{2} (x)

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

Apply radical rule:

a^{\frac{1}{n}} = n a

= 2 1 + sin^{2} (x)

Add a constant to the solution

= 2 1 + sin^{2} (x) + C

(25 + x^{2}) y^{^{'}} - 2 x y = 0

\frac{d y}{d x}, x y = 54

\frac{d}{d x} (x 3 x^{2})

\int_{0}^{N} e^{(- s t)} cos (3 t) d t

\frac{\partial}{\partial x} (x sin (x^{2} y))

What is the integral of (sin(2x))/(sqrt(1+sin^2(x))) ?
The integral of (sin(2x))/(sqrt(1+sin^2(x))) is 2sqrt(1+sin^2(x))+C