1
Calculer les intégales suivantes: \[\begin{array}{lll} \textbf{a)~} \displaystyle \int_{0^{}}^1\frac{\arctan x}{1+x^2}d x & \textbf{b)~} \displaystyle \int_{\frac 12}^2\left( 1+\frac 1{x^2}\right) \arctan x d x \quad & \textbf{c)~} \displaystyle \int_0^{\frac{\pi}{2}}x\sin x d x \\ \textbf{d)~} \displaystyle \int_{-1}^1\left( \arccos x\right) ^2 d x \quad & \textbf{e)~} \displaystyle \int_0^1\frac 1{\left( 1+x^2\right) ^2}d x & \textbf{f)~} \displaystyle \int_0^{\sqrt{3}}\frac{x^2}{\sqrt{4-x^2}}d x \\ \textbf{g)~}\displaystyle \int_1^2x^2\ln xd x & \textbf{h)~} \displaystyle \int_{-1}^1\frac 1{x^2+4x+7}d x & \textbf{i)~}\displaystyle \int_0^1\frac{ 3x+1}{\left( x+1\right) ^2}d x \end{array}\]