Hello here is it : $\displaystyle \int \frac{ x e^x }{ \sqrt{e^x+1} }dx$. by parts would be an idea. but it really hard to apply the integration by parts directly. any ideas??
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Originally Posted by TWiX Hello here is it : $\displaystyle \int \frac{ x e^x }{ \sqrt{e^x+1} }dx$. by parts would be an idea. but it really hard to apply the integration by parts directly. any ideas?? $\displaystyle \ln(z)=x$ then $\displaystyle \sqrt{z+1}=m$
Originally Posted by TWiX Hello here is it : $\displaystyle \int \frac{ x e^x }{ \sqrt{e^x+1} }dx$. by parts would be an idea. but it really hard to apply the integration by parts directly. any ideas?? use $\displaystyle x=ln(t)$ to get: $\displaystyle \int \frac{ln(t)}{\sqrt{t+1}}dt$. use $\displaystyle t+1=w^2$ to get: $\displaystyle 2\int ln(w^2-1) dw = 2\int ln(w+1) dw + 2 \int ln(w-1) dw$. two quick "by parts" will kill it.
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