ملتقى الفيزيائيين العرب - عرض مشاركة واحدة

زولديك · #8 21-11-2010, 13:34

${\color{blue} \int \frac{\sqrt{x+1}-1}{\sqrt{x+1}+1}dx=} {\color{blue} \int \frac{\sqrt{x+1}+1-2}{\sqrt{x+1}+1}dx=} {\color{blue} \int dx-2\int \frac{1}{\sqrt{x+1}+1}dx}$

${\color{blue} x=s^{2}-1\Rightarrow \dx=2sds \therefore -4[\int \frac{s+1}{s+1} ds-\int \frac{1}{s+1}ds]}$

${\color{blue} \therefore \int \frac{\sqrt{x+1}-1}{\sqrt{x+1}+1} dx=x-4(\sqrt{x+1})+4ln(\sqrt{x+1}+1)+C}$