What is the integral of pi/(1.2-2x) ?

The integral of pi/(1.2-2x) is -pi/2 ln|1.2-2x|+C

English

Español

Português

Français

Deutsch

Italiano

Русский

中文(简体)

한국어

日本語

Tiếng Việt

עברית

العربية

Popular >

integral of pi/(1.2-2x)

\int \frac{π}{1.2 - 2 x} d x

- \frac{π}{2} ln ∣ 1.2 - 2 x ∣ + C

Solution steps

\int \frac{π}{1.2 - 2 x} d x

Take the constant out:

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

= π \cdot \int \frac{1}{1.2 - 2 x} d x

Apply u-substitution

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

= π \cdot \int - \frac{1}{2 u} d u

Take the constant out:

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

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

Use the common integral:

\int \frac{1}{u} d u = ln (∣ u ∣)

= π (- \frac{1}{2} ln ∣ u ∣)

Substitute back

u = 1.2 - 2 x

= π (- \frac{1}{2} ln ∣ 1.2 - 2 x ∣)

Simplify

π (- \frac{1}{2} ln ∣ 1.2 - 2 x ∣) : - \frac{π}{2} ln ∣ 1.2 - 2 x ∣

= - \frac{π}{2} ln ∣ 1.2 - 2 x ∣

Add a constant to the solution

= - \frac{π}{2} ln ∣ 1.2 - 2 x ∣ + C

\frac{d}{d x} (18 - x^{2} - x)

f (x) = 10 x - x^{2}, g (x) = 3 x

n = 1 \sum \infty \frac{( 4 ^{n + 1} )}{5 ^{n}}

f (x) = \frac{1}{3} x^{3} - 5 x^{2} + 26 x + 23

\int y^{2} - x^{2} d x

What is the integral of pi/(1.2-2x) ?
The integral of pi/(1.2-2x) is -pi/2 ln|1.2-2x|+C