\everymath{\displaystyle}
Calculer les intégrales ou primitives suivantes:
\begin{multicols}{2}
 \begin{enumerate}
    \item  $\int_{1}^{27}\frac1{t\sqrt[3]{t}}dt$
    \item  $\int_{0}^2(1-\abs{x-1})^3 dx$
    \item  $\int_{0}^4\sqrt{2x+1}\ dx$
    \item  $\int_{0}^{1/2}x^3(1-x^2)^{5/2}dx$
    \item  $\int_{0}^1\frac1{\sqrt{9x^2+3}}\ dx$
    \item  $\int_{0}^{\frac{\pi}2}x^2\sin x e^x\ dx$
    \item  $\int\frac{\ln(\sin x)}{\cos^2x}\ dx$
    \item  $\int_{0}^{\frac{\pi}2}\frac1{3\tan x+2}\ dx$
    \item  $\int_{0}^{\pi}\frac1{a^2\cos^2x+\sin^2x}\ dx$
    \item  $\int\frac{\cos 2x}{\sin x+\sin 3x}\ dx$
   {\footnotesize (CV: $t=\cos x$)}
    \item  $\int\frac{1-\cos 2x}{\sin 3x}\ dx$
          {\footnotesize (CV: $t=\cos x$)}
    \item  $\int\frac{dx}{2\ch x+\sh x+1}$
          {\footnotesize (CV: $t=\th\frac{x}2$)}
    \item  $\int\frac{\sqrt{x+1}-\sqrt[3]{x+1}}{\sqrt{x+1}+\sqrt[3]{x+1}}\ dx$\\
   {\footnotesize (CV: $t=(x+1)^{1/6}$)}
    \item  $\int\frac{\sqrt{x^3+1}}x\ dx$
          {\footnotesize (CV: $\displaystyle t^2=x^3+1$)}
    \item  $\int\frac{x+1}{\sqrt{x(1-2x)}}\ dx$
          {\footnotesize (CV: $x-\frac14=\frac14\cos t$)}
    \item  $\int\sin2x\sh3x\ dx$
    \item  $\int \tan^5(x)\ dx$
    \item  $\int \frac{\sin x}{2+\tan^2x}\ dx$
    \item  $\int\frac1{\cos^4x+\sin^4x}\ dx$
 \end{enumerate}
\end{multicols}