Question 1

Durée : 5 mn

Note maximale : 5

Question

Calculer la primitive \(I_1=\int\text{cotan }^2xdx\)

Solution

\(I_1=\int\text{cotan }^2xdx=\int\frac{\cos^2x}{\sin^2x}dx\)

\(=\int\frac{1-\sin^2x}{\sin^2x}dx~~\color{red}\text{ (2 pts)}\)

\(=\int\frac{dx}{\sin^2x}-\int dx\)

donc

\(\color{blue}I_1 = - \text{cotan }x - x + C~~\color{red}\text{ (3 pts)}\)