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

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

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

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

arcsin (tan (x)) + C

Solution steps

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

Apply u-substitution

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

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

Use the common integral:

\int \frac{1}{1 - u ^{2}} d u = arcsin (u)

= arcsin (u)

Substitute back

u = tan (x)

= arcsin (tan (x))

Add a constant to the solution

= arcsin (tan (x)) + C

y^{^{''}} - 6 y^{^{'}} = 36 t

n = 0 \sum \infty \frac{n !}{2 ^{n}}

x \to - \infty lim (x^{2} e x)

\frac{\partial}{\partial y} (4 - x^{2} - 2 y^{2})

\frac{d}{d x} (\frac{x - 2 ln ( x ) - 1}{x - 1})

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