What is the integral of (10)/(cos(θ)-1) ?

The integral of (10)/(cos(θ)-1) is 10cot(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 (10)/(cos(θ)-1)

\int \frac{10}{cos ( θ ) - 1} d θ

10 cot (\frac{θ}{2}) + C

Solution steps

\int \frac{10}{cos ( θ ) - 1} d θ

Take the constant out:

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

= 10 \cdot \int \frac{1}{cos ( θ ) - 1} d θ

Apply u-substitution

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

= 10 \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

= 10 (- \int \frac{1}{u ^{2}} d u)

Apply the Power Rule

: - \frac{1}{u}

= 10 (- (- \frac{1}{u}))

Substitute back

u = tan (\frac{θ}{2})

= 10 (- (- \frac{1}{tan ( \frac{θ}{2} )}))

Simplify

10 (- (- \frac{1}{tan ( \frac{θ}{2} )})) : 10 cot (\frac{θ}{2})

= 10 cot (\frac{θ}{2})

Add a constant to the solution

= 10 cot (\frac{θ}{2}) + C

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

\int 5 + 4 x^{2} d x

ln (2^{x} - 4)

\frac{\partial}{\partial y} (3 cos (x) - sin (x) y)

y = (25 - 4 x^{2})^{2}, x = - \frac{5}{2}, x = \frac{5}{2}

What is the integral of (10)/(cos(θ)-1) ?
The integral of (10)/(cos(θ)-1) is 10cot(θ/2)+C