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

The integral of 1/((sin(x)cos^2(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

Popular >

integral of 1/((sin(x)cos^2(x)))

integral

\frac{1}{( sin ( x ) cos ^{2} ( x ) )}

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

Solution steps

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

Rewrite using trig identities

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

Apply Integration By Parts

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

= 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

x^{3} - x^{2}

(\frac{t - 1}{t})^{2}

\frac{1}{( x + 1 ) ^{3}}

e^{\frac{1}{y}}

sin (- 2 x + 1)

What is the integral of 1/((sin(x)cos^2(x))) ?
The integral of 1/((sin(x)cos^2(x))) is sec(x)+ln|tan(x/2)|+C