Is the answer 18 ? @Sourav_Dey sir ?

# Thread to share Good Questions from Calculus which requires deep thinking

Yes @ Mayank ... share your approach !

First removed the x^2 from the denominator by substituting x^3 = t

So numerator is

\int^{1}_{0} lnx ln(1-x) dx

and denominator is

1 \over 9 \int^{0.5}_{0} lnx ln(1-x) dx

Now we can clearly see that the integral in numerator is twice that of in denominator

So we get 18

Which package is this archive or revision or which ?

It's archive

No check again

The Integral is \frac{I_{n+1}}{I_{n}}

Limits from pi/4 to 3pi/4 integral of sin

Now we can use reduction formula maybe?

@Mayank_Chowdhary what did you get

i did the same and got an infinite series

something like

n(n-2)(n-4).../ (n+1)(n-1)(n-3).... the whole squared with a root 2 outside it

@Mayank_Chowdhary yes √2 is correct .. submit your solution

@Siddhant_Mudholkar which question solution do you ask me ?

I am also getting \color{brown}\sqrt{2}.

Yes Ur approach sir