What is the integral of (5ln(x))/(x^3) ?

The integral of (5ln(x))/(x^3) is 5(-(ln(x))/(2x^2)-1/(4x^2))+C

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integral of (5ln(x))/(x^3)

\int \frac{5 ln ( x )}{x ^{3}} d x

5 (- \frac{ln ( x )}{2 x ^{2}} - \frac{1}{4 x ^{2}}) + C

Solution steps

\int \frac{5 ln ( x )}{x ^{3}} 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 )}{x ^{3}} d x

Apply Integration By Parts

: - \frac{ln ( x )}{2 x ^{2}} - \int - \frac{1}{2 x ^{3}} d x

= 5 (- \frac{ln ( x )}{2 x ^{2}} - \int - \frac{1}{2 x ^{3}} d x)

\int - \frac{1}{2 x ^{3}} d x = \frac{1}{4 x ^{2}}

= 5 (- \frac{ln ( x )}{2 x ^{2}} - \frac{1}{4 x ^{2}})

Add a constant to the solution

= 5 (- \frac{ln ( x )}{2 x ^{2}} - \frac{1}{4 x ^{2}}) + C

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\frac{d y}{d x} = sin (x + y) + cos (x + y)

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What is the integral of (5ln(x))/(x^3) ?
The integral of (5ln(x))/(x^3) is 5(-(ln(x))/(2x^2)-1/(4x^2))+C