Question

Integral of ln(x^3 - x) dx

Answer 1

by parts\[u=\ln(x^3-x)\\dv=dx\]

Answer 2

try doing what TuringTest did

Answer 3

\[\int\limits \ln \left( x^3-x \right) *1~ dx=\ln \left( x^3-x \right)x-\int\limits \frac{( 3x^2-x) }{x^3-x } *x~dx\]
\[\int\limits \frac{ \left(3x^2-x \right) }{x \left( x^2-1 \right) }*x~dx=\int\limits \frac{ 3x^2-x }{x^2-1 } dx\]
\[\frac{ 3x^2-x }{\left( x+1 \right)\left( x-1 \right) }=3+\frac{ 3\left( -1 \right)^2-(-1) }{ \left( x+1 \right)\left( -1-1 \right) }+\frac{3(1)^2-1 }{ \left(1+1 \right)\left( x-1 \right) }\]
\[=3+\frac{ 4 }{-2\left( x+1 \right) }+\frac{ 2 }{2\left( x-1 \right) }=3-\frac{ 2 }{x+1 }+\frac{ 1 }{x-1 }\]
now you can complete.