What is the integral of 1/(cos^2(x)sqrt(tan(x))) ?

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

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integral of 1/(cos^2(x)sqrt(tan(x)))

\int \frac{1}{cos ^{2} ( x ) tan ( x )} d x

2 tan (x) + C

Solution steps

\int \frac{1}{cos ^{2} ( x ) tan ( 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 = tan (x)

= 2 tan^{\frac{1}{2}} (x)

Apply radical rule:

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

= 2 tan (x)

Add a constant to the solution

= 2 tan (x) + C

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