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

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

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

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

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

Solution steps

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

Take the constant out:

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

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

Apply Integration By Parts

: - \frac{ln ( x )}{x} - \int - \frac{1}{x ^{2}} d x

= 8 (- \frac{ln ( x )}{x} - \int - \frac{1}{x ^{2}} d x)

\int - \frac{1}{x ^{2}} d x = \frac{1}{x}

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

Add a constant to the solution

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

\frac{d}{d x} (\frac{( 40 x ^{5} )}{e ^{x}})

t^{2} \frac{d y}{d t} - t = 1 + y + t y, y (1) = 4

\frac{\partial}{\partial x} (x ln (x y))

\int \frac{4}{x ^{2} + 9} d x

y^{^{''}} - 4 y^{^{'}} + 4 y = 6 t^{2} e^{2 t}

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