What is the integral of 1/((100-n)) ?

The integral of 1/((100-n)) is -ln|100-n|+C

English

Español

Português

Français

Deutsch

Italiano

Русский

中文(简体)

한국어

日本語

Tiếng Việt

עברית

العربية

Popular >

integral of 1/((100-n))

integral

\frac{1}{( 100 - n )}

- ln ∣ 100 - n ∣ + C

Solution steps

\int \frac{1}{100 - n} d n

Apply u-substitution

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

= \int - \frac{1}{u} d u

Take the constant out:

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

= - \int \frac{1}{u} d u

Use the common integral:

\int \frac{1}{u} d u = ln (∣ u ∣)

= - ln ∣ u ∣

Substitute back

u = 100 - n

= - ln ∣ 100 - n ∣

Add a constant to the solution

= - ln ∣ 100 - n ∣ + C

\frac{- 1}{x ^{3}}

a + 3 c - 2 d

(1 - 0.1 x)^{- 2}

5 - (\frac{8}{x ^{2}})

2 x^{3} (e^{x})^{- 2}

What is the integral of 1/((100-n)) ?
The integral of 1/((100-n)) is -ln|100-n|+C