integral for a strong jee contender

Ï€/4 ln√2?

it is correct [1]

\int_{0}^{1}{\frac{log(1+x)}{x}}dx

this one is also nice

Ï€ ²6 , ain ' t it Qwerty ?

Edit : A small mistake , the correct ans. is , I = Î ²12

ricky i think u hav made a small calc mistake , ans is Ï€²/12

the 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}

can u plss post the soln ...m not actually getting the method how u solved it