What is the integral of 1/(cos(x)cot(x)) ?

The integral of 1/(cos(x)cot(x)) is sec(x)+C

English

Español

Português

Français

Deutsch

Italiano

Русский

中文(简体)

한국어

日本語

Tiếng Việt

עברית

العربية

integral of 1/(cos(x)cot(x))

\int \frac{1}{cos ( x ) cot ( x )} d x

sec (x) + C

Solution steps

\int \frac{1}{cos ( x ) cot ( x )} d x

Rewrite using trig identities

= \int sec (x) tan (x) d x

Apply u-substitution

= \int 1 d u

Integral of a constant:

\int a d x = a x

= 1 \cdot u

Substitute back

u = sec (x)

= 1 \cdot sec (x)

Simplify

= sec (x)

Add a constant to the solution

= sec (x) + C

\int \frac{x - 7}{2 x ^{2} - 7 x} d x

\int \frac{5 x + 8}{x ^{2} + 3 x + 2} d x

\int \frac{4}{( x ^{2} + 2 ^{2} ) ^{1}} d x

\int \frac{x \cdot arctan ( x )}{( 1 + x ^{2} ) ^{2}} d x

\int (3 - 4 w) (4 w^{2} - 6 w + 7)^{10} d w

What is the integral of 1/(cos(x)cot(x)) ?
The integral of 1/(cos(x)cot(x)) is sec(x)+C