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

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

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integral of (sqrt(tan(x)))/(sin^2(x))

integral

\frac{tan ( x )}{sin ^{2} ( x )}

- 2 cot (x) + C

Solution steps

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

Apply u-substitution

: \int \frac{1}{u ^{\frac{3}{2}}} d u

= \int \frac{1}{u ^{\frac{3}{2}}} d u

Apply the Power Rule

: - \frac{2}{u}

= - \frac{2}{u}

Substitute back

u = tan (x)

= - \frac{2}{tan ( x )}

Use the basic trigonometric identity:

\frac{1}{tan ( x )} = cot (x)

= - 2 cot (x)

Add a constant to the solution

= - 2 cot (x) + C

\frac{x ^{2}}{4 a + 2 a}

\frac{( x - 1 )}{( x ^{2} + 1 )}

\frac{1}{( x ^{2} - 4 )}

\frac{4 x ^{4}}{( 1 + x ^{2} )}

\frac{4 t}{3 t ^{2} - 7}

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