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

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

Popular >

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

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

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

Solution steps

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

Apply Integration By Parts

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

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

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

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

\frac{ln ( x ^{2} )}{2 x ^{2}} = \frac{ln ( x )}{x ^{2}}

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

Add a constant to the solution

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

\frac{d}{d x} (3 - x)

\int \frac{1}{8 + x ^{2}} d x

\int_{5}^{- 5} \frac{1}{∣ x ∣ ^{(\frac{2}{3})}} d x

n = 0 \sum \infty \frac{ln ( n )}{n !}

y^{^{''}} - 4 y^{^{'}} + 3 y = 0, y (0) = 3, y^{^{'}} (0) = 2

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