1-calculate-I-ln-1-t-1-t-dt-2-find-0-1-ln-1-t-1-t-dt-

Question Number 48495 by maxmathsup by imad last updated on 24/Nov/18

1) c a l c u l a t e I = \int \frac{l n (1 + t)}{1 + t} d t

2) f i n d \int_{0}^{1} \frac{l n (1 + t)}{1 + t} d t

Commented by maxmathsup by imad last updated on 25/Nov/18

b y p a r t s u^{^{'}} = \frac{1}{1 + t} a n d v = l n (1 + t) \Rightarrow I = {l n}^{2} (1 + t) - \int \frac{l n (t)}{1 + t} d t = {l n}^{2} (1 + t) - I \Rightarrow

2 I = {l n}^{2} (1 + t) \Rightarrow I = \frac{1}{2} {l n}^{2} (1 + t) + c

2) \int_{0}^{1} \frac{l n (1 + t)}{1 + t} d t = {[\frac{1}{2} {l n}^{2} (1 + t)]}_{0}^{1} = \frac{1}{2} {l n}^{2} (2) .

Answered by Abdulhafeez Abu qatada last updated on 25/Nov/18