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

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

Popular >

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

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

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

Solution steps

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

Apply Integration By Parts

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

= 3 (- \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}}

= 3 (- \frac{ln ( x )}{2 x ^{2}} - \frac{1}{4 x ^{2}})

Add a constant to the solution

= 3 (- \frac{ln ( x )}{2 x ^{2}} - \frac{1}{4 x ^{2}}) + C

\frac{d}{d x} (arcsin (\frac{x}{7}))

\frac{\partial}{\partial x} (x e^{x y} - \frac{x}{y ^{2}})

\frac{( 8 e ^{(9 x)} )}{( 5 x - 2 )}

\frac{d}{d x} (x e^{7 x})

\int (2 x + 1) d x

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