What is the integral of (3ln(x+7))/(x^2) ?

The integral of (3ln(x+7))/(x^2) is 3(-(ln(x+7))/x+1/7 ln|x|-1/7 ln|x+7|)+C

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integral of (3ln(x+7))/(x^2)

\int \frac{3 ln ( x + 7 )}{x ^{2}} d x

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

Solution steps

\int \frac{3 ln ( x + 7 )}{x ^{2}} d x

Take the constant out:

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

= 3 \cdot \int \frac{ln ( x + 7 )}{x ^{2}} d x

Apply Integration By Parts

: - \frac{ln ( x + 7 )}{x} - \int - \frac{1}{x ( x + 7 )} d x

= 3 (- \frac{ln ( x + 7 )}{x} - \int - \frac{1}{x ( x + 7 )} d x)

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

= 3 (- \frac{ln ( x + 7 )}{x} - (- \frac{1}{7} ln ∣ x ∣ + \frac{1}{7} ln ∣ x + 7 ∣))

Simplify

= 3 (- \frac{ln ( x + 7 )}{x} + \frac{1}{7} ln ∣ x ∣ - \frac{1}{7} ln ∣ x + 7 ∣)

Add a constant to the solution

= 3 (- \frac{ln ( x + 7 )}{x} + \frac{1}{7} ln ∣ x ∣ - \frac{1}{7} ln ∣ x + 7 ∣) + C

\frac{1}{3 x ^{2} + 4 x}

\frac{\partial}{\partial x} (\frac{9 x y ^{2}}{x ^{2} + y ^{4}})

\frac{d}{d x} ((4 x^{2} + 3 x + 2)^{5})

\int_{0}^{2} \frac{6 x}{( 1 + x ^{2} ) ^{2}} d x

\frac{\partial}{\partial y} (y - x^{3})

What is the integral of (3ln(x+7))/(x^2) ?
The integral of (3ln(x+7))/(x^2) is 3(-(ln(x+7))/x+1/7 ln|x|-1/7 ln|x+7|)+C