What is the integral of 2/(cos(θ)-1) ?

The integral of 2/(cos(θ)-1) is 2cot(θ/2)+C

English

Español

Português

Français

Deutsch

Italiano

Русский

中文(简体)

한국어

日本語

Tiếng Việt

עברית

العربية

Popular >

integral of 2/(cos(θ)-1)

\int \frac{2}{cos ( θ ) - 1} d θ

2 cot (\frac{θ}{2}) + C

Solution steps

\int \frac{2}{cos ( θ ) - 1} d θ

Take the constant out:

\int a \cdot f (x) d x = a \cdot \int f (x) d x

= 2 \cdot \int \frac{1}{cos ( θ ) - 1} d θ

Apply u-substitution

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

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

Take the constant out:

\int a \cdot f (x) d x = a \cdot \int f (x) d x

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

Apply the Power Rule

: - \frac{1}{u}

= 2 (- (- \frac{1}{u}))

Substitute back

u = tan (\frac{θ}{2})

= 2 (- (- \frac{1}{tan ( \frac{θ}{2} )}))

Simplify

2 (- (- \frac{1}{tan ( \frac{θ}{2} )})) : 2 cot (\frac{θ}{2})

= 2 cot (\frac{θ}{2})

Add a constant to the solution

= 2 cot (\frac{θ}{2}) + C

\int \frac{x + 7}{x ^{2} - 8 x - 19} d x

\int cos (7 t) cos (3 t) d t

cot^{4} (\frac{1}{2}) x

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

\int \frac{x - 4}{x ^{2} + x} d x

What is the integral of 2/(cos(θ)-1) ?
The integral of 2/(cos(θ)-1) is 2cot(θ/2)+C