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

The integral of (7ln(x))/(x^3) is 7(-(ln(x))/(2x^2)-1/(4x^2))+C

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

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

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

Solution steps

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

Apply Integration By Parts

= 7 (- \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}}

= 7 (- \frac{ln ( x )}{2 x ^{2}} - \frac{1}{4 x ^{2}})

Add a constant to the solution

= 7 (- \frac{ln ( x )}{2 x ^{2}} - \frac{1}{4 x ^{2}}) + C

What is the integral of (7ln(x))/(x^3) ?
The integral of (7ln(x))/(x^3) is 7(-(ln(x))/(2x^2)-1/(4x^2))+C