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

The integral of (sec^2(x))/(sin(x)) is sec(x)+ln|tan(x/2)|+C

English

Español

Português

Français

Deutsch

Italiano

Русский

中文(简体)

한국어

日本語

Tiếng Việt

עברית

العربية

integral of (sec^2(x))/(sin(x))

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

sec (x) + ln tan (\frac{x}{2}) + C

Solution steps

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

Apply Integration By Parts

= sec (x) - \int - cot (x) csc (x) tan (x) d x

\int - cot (x) csc (x) tan (x) d x = - ln tan (\frac{x}{2})

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

Simplify

= sec (x) + ln tan (\frac{x}{2})

Add a constant to the solution

= sec (x) + ln tan (\frac{x}{2}) + C

What is the integral of (sec^2(x))/(sin(x)) ?
The integral of (sec^2(x))/(sin(x)) is sec(x)+ln|tan(x/2)|+C