całka pierwiastek e do x - 1

[GrazynkaUTP]

Oblicz
\(\displaystyle{ \int_{}^{} \sqrt{ e^{x} -1 } dx}\)
podstawiam za
\(\displaystyle{ \left| \sqrt{ e^{x} -1 } = t\right|}\) \(\displaystyle{ \Rightarrow}\) \(\displaystyle{ e^{x} = t^{2} + 1}\)
\(\displaystyle{ \left| \frac{e^{x}}{2 \sqrt{e^{x} - 1 } } dx = dt \right|}\)
\(\displaystyle{ \left| dx= \frac{2t}{t^{2} + 1}dt\right|}\)
\(\displaystyle{ \int_{}^{} \frac{2t ^{2} }{t ^{2} +1} dt}\)

i co dalej?

[miodzio1988]

\(\displaystyle{ t ^{2}=t ^{2}+1-1}\)

[GrazynkaUTP]

a no tak, dziękuje