Exercice $4.$ Calculate the following indefinite integrals : ${\displaystyle \underset{\phantom{}}{\overset{\phantom{}}{}}}\frac{dx}{x^2+2x+5}{\displaystyle \underset{\phantom{}}{\overset{\phantom{}}{}}}\frac{dx}{x^2-6x+5}{\displaystyle \underset{\phantom{}}{\overset{\phantom{}}{}}}\frac{dx}{\sqrt[\phantom{2}]{2-3x-4x^2}}{\displaystyle \underset{\phantom{}}{\overset{\phantom{}}{}}}\frac{dx}{\sqrt[\phantom{2}]{x^2+x+1}}{\displaystyle \underset{\phantom{}}{\overset{\phantom{}}{}}}\frac{x+3}{\sqrt[\phantom{2}]{4x^2+4x+3}}dx{\displaystyle \underset{\phantom{}}{\overset{\phantom{}}{}}}\frac{3x-1}{x^2-x+1}dx{\displaystyle \underset{\phantom{}}{\overset{\phantom{}}{}}}\frac{x^2+2}{x^3+1}dx{\displaystyle \underset{\phantom{}}{\overset{\phantom{}}{}}}\frac{2x^2}{x-1}dx{\displaystyle \underset{\phantom{}}{\overset{\phantom{}}{}}}si{n}^8(x)co{s}^3(x)dx{\displaystyle \underset{\phantom{}}{\overset{\phantom{}}{}}}si{n}^6(x)dx{\displaystyle \underset{\phantom{}}{\overset{\phantom{}}{}}}\frac{\sqrt[\phantom{2}]{x^3}-\sqrt[3]{x}}{6\sqrt[4]{x}}dx{\displaystyle \underset{\phantom{}}{\overset{\phantom{}}{}}}c{h}^6(x)dx$ Exercice $5.$ Let the integral $I_n={\displaystyle \underset{\phantom{}}{\overset{\phantom{}}{}}}\frac{dx}{co{s}^n(x)}.$ Find an recurente relation between $I_n$