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

The integral of 1/(sin^2(x)cos(x)) is -csc(x)+ln|tan(x)+sec(x)|+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^2(x)cos(x))

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

- csc (x) + ln ∣ tan (x) + sec (x) ∣ + C

Solution steps

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

Rewrite using trig identities

= \int \frac{csc ^{2} ( x )}{cos ( x )} d x

Apply Integration By Parts

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

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

\int - sec (x) d x = - ln ∣ tan (x) + sec (x) ∣

= - csc (x) - (- ln ∣ tan (x) + sec (x) ∣)

Simplify

= - csc (x) + ln ∣ tan (x) + sec (x) ∣

Add a constant to the solution

= - csc (x) + ln ∣ tan (x) + sec (x) ∣ + C

2 x, 4 x^{2}

\int (sin (x))^{4} (cos (x))^{2} d x

\frac{\partial}{\partial x} (x ln (\frac{x}{y}))

\int cos (2 x) sin (x) d x

\int (∣ x ∣ + 1) d x

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