Question

integrate ln(x).(x^-1/5)

Answer 1

i got to this point \[(5/4)x ^{4/5}.\ln x-\int\limits5x ^{4/5}/4x\]

Answer 2

then i'm commiting a mistake that i still don't know what it is and cause of that can't reach the result.

Answer 3

\[Let I=\int\limits \ln \left( x \right).x ^{-\frac{ 1 }{ 5 }}dx=\ln x*\frac{ x ^{-\frac{ 1 }{ 5}+1 } }{-\frac{ 1 }{ 5 }+1 }-\int\limits \frac{ 1 }{x }*\frac{ x ^{^{\frac{ -1 }{ 5 }+1}} }{ \frac{ -1 }{5 }+1 }dx+c\]\]
\[=\frac{ x ^{\frac{ 4 }{ 5 }} }{ \frac{ 4 }{ 5 } }\ln x-\frac{ 5 }{4 } \int\limits x ^{\frac{ -1 }{ 5 }} dx+c =\frac{ 5 }{ 4 }x ^{\frac{ 4 }{5 }}\ln x-\frac{ 5 }{ 4} \frac{ x ^{\frac{ -1 }{5 }+1} }{ \frac{ -1 }{5 }+1 } +c \]
solve it and get the solution

Answer 4

you followed or should I complete.

Answer 5

Thanks. I forgot to divide \[x^{4/5}\] for \[x\] and to put the \[5/4\] out of the integration. The answer is \[(5/4)x ^{4/5}.\ln x - (25/16)x ^{4/5}+C\].

Answer 6

correct.