Exercices corrigés
| Exercice 1. Calculer les primitives :\begin{array}{c}\displaystyle\int\dfrac{x-1}{\sqrt x}{\,\text{d}x}\quad\displaystyle\int x^2(1-\sqrt[3]{x})\,\text{d}x\\\\\displaystyle\int\dfrac{(1-\sqrt x)^2}{\sqrt[3]{x}}\,\text{d}x\end{array} |
| Exercice 2. Calculer les primitives : {\begin{array}{c}\displaystyle\int\Bigl(1-\dfrac1{\sqrt[3]{x}}\Bigr)^2\,\text{d}x\quad\displaystyle\int\Bigl(x^2+\dfrac1{x^2}\Bigr)^2\,\text{d}x\\\\\displaystyle\int\dfrac{\,\text{d}x}{\sqrt{x}+\sqrt{x-1}}\end{array}} |
| Exercice 3. Calculer les primitives : {\begin{array}{c}\displaystyle\int\sin^3x\cos x\,\text{d}x\quad\displaystyle\int\sin^3x\cos x\,\text{d}x\\\\\displaystyle\int\dfrac{\sin x\,\text{d}x}{\cos^2 x}\end{array}} |
| Exercice 4. Calculer les primitives : {\begin{array}{c}\displaystyle\int x(1+x^2)^5\,\text{d}x\quad\displaystyle\int x^2\sqrt{1+x^3}\,\text{d}x\\\\\displaystyle\int\tan x\,\text{d}x\end{array}} |
| Exercice 5. Calculer les primitives : {\displaystyle\int\dfrac{\,\text{d}x}{x(x^2+1)^2}\;\text{et}\;\displaystyle\int\dfrac{\,\text{d}x}{x(x^5+1)^2}} |
| Exercice 6. Calculer les primitives : {\begin{array}{cc}\displaystyle\int\dfrac{\text{d}x}{\sin(x)}&\displaystyle\int\dfrac{2\cos(x)\,\text{d}x}{3-\cos(2x)}\\\\\displaystyle\int\dfrac{\,\text{d}x}{\sin(x)\cos(x)}&\displaystyle\int\dfrac{\text{d}x}{1+\sin(x)}\end{array}} |
| Exercice 7. Calculer les primitives : {\displaystyle\int\dfrac{x\,\text{d}x}{\sqrt{x+1}}\;\text{et}\;\displaystyle\int\dfrac{\,\text{d}x}{(x(2-x))^{3/2}}} |