23\int_{0}^{1}{\frac{log(1+x)}{x}}dx
this one is also nice
not much tough
\int_{0}^{1}\frac{\ln(1+x)}{1+x^{2}}\mathrm{dx}
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7 Answers
1Ï€ 26 , ain ' t it Qwerty ?
Edit : A small mistake , the correct ans. is , I = Î 212
1the common trick to solve definite integral involving logarithms is 'differentiation under integral sign'
for qwerty's integral I(a)=\int_{0}^{1}{\frac{\log(1+ax)}{x}\mathrm{dx}}\\ I'(a)=\int_0^1\frac{\mathrm{dx}}{(1+ax)x} \\ \texttt{now carry out the integral using partial fractions}\\ \texttt{and use I(0)=0 to calculate the integration constant}
1can u plss post the soln ...m not actually getting the method how u solved it