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

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

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

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

2 tan (x) - 1 + C

Solution steps

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

Apply u-substitution

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

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

Apply u-substitution

: \int 2 d v

= \int 2 d v

Integral of a constant:

\int a d x = a x

= 2 v

Substitute back

= 2 tan (x) - 1

Add a constant to the solution

= 2 tan (x) - 1 + C

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