What is the integral of (5ln(x+8))/(x^2) ?

The integral of (5ln(x+8))/(x^2) is 5(-(ln(x+8))/x+1/8 ln|x|-1/8 ln|x+8|)+C

English

Español

Português

Français

Deutsch

Italiano

Русский

中文(简体)

한국어

日本語

Tiếng Việt

עברית

العربية

Popular >

integral of (5ln(x+8))/(x^2)

\int \frac{5 ln ( x + 8 )}{x ^{2}} d x

5 (- \frac{ln ( x + 8 )}{x} + \frac{1}{8} ln ∣ x ∣ - \frac{1}{8} ln ∣ x + 8 ∣) + C

Solution steps

\int \frac{5 ln ( x + 8 )}{x ^{2}} d x

Take the constant out:

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

= 5 \cdot \int \frac{ln ( x + 8 )}{x ^{2}} d x

Apply Integration By Parts

: - \frac{ln ( x + 8 )}{x} - \int - \frac{1}{x ( x + 8 )} d x

= 5 (- \frac{ln ( x + 8 )}{x} - \int - \frac{1}{x ( x + 8 )} d x)

\int - \frac{1}{x ( x + 8 )} d x = - \frac{1}{8} ln ∣ x ∣ + \frac{1}{8} ln ∣ x + 8 ∣

= 5 (- \frac{ln ( x + 8 )}{x} - (- \frac{1}{8} ln ∣ x ∣ + \frac{1}{8} ln ∣ x + 8 ∣))

Simplify

= 5 (- \frac{ln ( x + 8 )}{x} + \frac{1}{8} ln ∣ x ∣ - \frac{1}{8} ln ∣ x + 8 ∣)

Add a constant to the solution

= 5 (- \frac{ln ( x + 8 )}{x} + \frac{1}{8} ln ∣ x ∣ - \frac{1}{8} ln ∣ x + 8 ∣) + C

sin (x) - x

y^{^{''}} + 4 y = 20 sin (2 t)

f (x) = \frac{5 x}{x + 3}, (2, 2)

13.375 ln (\frac{x}{x - 1250})

\int 6 x (1 - x) d x

What is the integral of (5ln(x+8))/(x^2) ?
The integral of (5ln(x+8))/(x^2) is 5(-(ln(x+8))/x+1/8 ln|x|-1/8 ln|x+8|)+C