What is the integral of 7/(x-3) ?

The integral of 7/(x-3) is 7ln|x-3|+C

English

Español

Português

Français

Deutsch

Italiano

Русский

中文(简体)

한국어

日本語

Tiếng Việt

עברית

العربية

Popular >

integral of 7/(x-3)

\int \frac{7}{x - 3} d x

7 ln ∣ x - 3 ∣ + C

Solution steps

\int \frac{7}{x - 3} d x

Take the constant out:

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

= 7 \cdot \int \frac{1}{x - 3} d x

Apply u-substitution

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

= 7 \cdot \int \frac{1}{u} d u

Use the common integral:

\int \frac{1}{u} d u = ln (∣ u ∣)

= 7 ln ∣ u ∣

Substitute back

u = x - 3

= 7 ln ∣ x - 3 ∣

Add a constant to the solution

= 7 ln ∣ x - 3 ∣ + C

y^{^{'}} = \frac{2 x sec ( \frac{y}{x} ) + y}{x}

\frac{d}{d x} (\frac{x - 4}{3})

y = 4 x^{3} e^{- x}

\int (- \frac{x ^{3}}{3} - x^{2} + \frac{4}{3}) d x

f (x) = e^{x}, x = 0