\(\int_{-\infty}^{+\infty} \frac{ d t}{e^t+t^2e^{-t}}\) (cv)
\(\int_1^{+\infty} \frac{ e^{\sin t}}{t} \,d t\) (dv)
\(\int_0^1 \frac{ t^\alpha-1}{\ln{t}} \,d t\) (cv ssi \(\alpha > -1\))
\(\int_{e^2}^{+\infty} \frac{ d t}{t(\ln t)(\ln\ln t)}\) (dv)
\(\int_0^{+\infty} \ln\Bigl( \frac{1+t^2}{1+t^3} \Bigr) \,d t\) (dv)
\(\int_0^{+\infty} \Bigl(2+(t+3)\ln\bigl(\frac{ t+2}{t+4} \bigr)\Bigr) d t\) (cv)
\(\int_0^{+\infty} \frac{ {t\ln t}}{(1+t^2)^\alpha{}} \,d t\) (cv ssi \(\alpha > 1\))
\(\int_0^1 \frac{ d t}{1-\sqrt t}\) (dv)
\(\int_0^{+\infty} \frac{ (t+1)^\alpha-t^\alpha}{t^\beta} \,d t\) (cv ssi \(0 < \beta-\alpha < 1\) ou \(\alpha = 0\))
\(\int_0^{+\infty} \sin(t^2)\,d t\) (cv)
\(\int_0^1 \frac{ d t}{\arccos{t}}\) (cv)
\(\int_0^{+\infty} \frac{ \ln(\Arctan{t})}{t^\alpha} \,d t\) (dv)
\(\int_1^{+\infty} \frac{ {\ln(1+1/t)\,d t}}{(t^2-1)^\alpha}\) (cv ssi \(0<\alpha<1\))
\(\int_0^1 \frac{ |\ln{t}|^\beta}{(1-t)^\alpha} \,d t\) (cv ssi \(\alpha < \beta+1\))
\(\int_0^{+\infty} t^\alpha\bigl(1-e^{-1}{\sqrt t}\bigr)\,d t\) (cv ssi \(-1<\alpha<-\frac 12\))
\(\int_0^1 \sin\bigl(\frac1t\bigr)e^{-1}{t}t^{-k}\,d t\) (cv)