exo7 2326

Calculer les intégrales suivantes : $$\begin{aligned} && \int_1^e {t^n \ln^4 t}\,dt, \qquad n \neq -1, \\ && \int_0^1 {dt \over {\sqrt{x} (1+\sqrt[3]{x})^2}}, \\ && \int_a^b \sqrt{(t-a)(t-b)}\,dt, \\ && \int_0^1 2^t \cdot 3^{2t} \cdot 5^{3t}\,dt, \\ && \int_0^1 {dt \over {\sqrt{x^2 +2x +5}}}, \\ && \int_{-\pi}^\pi \sqrt{1+\cos t}\,dt, \\ && \int_0^1 t^7 \arctan t\,dt. \end{aligned}$$