What is the integral of (7ln(x+8))/(x^2) ?

The integral of (7ln(x+8))/(x^2) is 7(-(ln(x+8))/x+1/8 ln|x|-1/8 ln|x+8|)+C

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integral of (7ln(x+8))/(x^2)

\int \frac{7 ln ( x + 8 )}{x ^{2}} d x

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

Solution steps

\int \frac{7 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

= 7 \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

= 7 (- \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 ∣

= 7 (- \frac{ln ( x + 8 )}{x} - (- \frac{1}{8} ln ∣ x ∣ + \frac{1}{8} ln ∣ x + 8 ∣))

Simplify

= 7 (- \frac{ln ( x + 8 )}{x} + \frac{1}{8} ln ∣ x ∣ - \frac{1}{8} ln ∣ x + 8 ∣)

Add a constant to the solution

= 7 (- \frac{ln ( x + 8 )}{x} + \frac{1}{8} ln ∣ x ∣ - \frac{1}{8} ln ∣ x + 8 ∣) + C

\frac{d y}{d x} - 2 x y = 10, y (0) = - 8

\int_{2}^{4} 4 (3 x - 1) d x

y^{^{''}} - 100 y = 0

\frac{d}{d x} (\frac{1}{x ^{2} - 3 x + 2})

4 y^{^{'}} - 12 x^{2} = 0

What is the integral of (7ln(x+8))/(x^2) ?
The integral of (7ln(x+8))/(x^2) is 7(-(ln(x+8))/x+1/8 ln|x|-1/8 ln|x+8|)+C