Intégrale de $\sec^{2}{\left(x \right)}$

Trouvez $\int \sec^{2}{\left(x \right)}\, dx$.

The integral of $\sec^{2}{\left(x \right)}$ is $\int{\sec^{2}{\left(x \right)} d x} = \tan{\left(x \right)}$:

$${\color{red}{\int{\sec^{2}{\left(x \right)} d x}}} = {\color{red}{\tan{\left(x \right)}}}$$

C'est pourquoi,

$$\int{\sec^{2}{\left(x \right)} d x} = \tan{\left(x \right)}$$

Ajouter la constante d'intégration :

$$\int{\sec^{2}{\left(x \right)} d x} = \tan{\left(x \right)}+C$$

Answer: $\int{\sec^{2}{\left(x \right)} d x}=\tan{\left(x \right)}+C$