[tex]\left\{\begin{matrix} u=ln(x+\sqrt{x^2+1}) & \\ dv=\frac{x}{\sqrt{x^2+1}}dx & \end{matrix}\right.\rightarrow \left\{\begin{matrix} du=\frac{1+\frac{x}{\sqrt{x^2+1}}}{x+\sqrt{x^2+1}}dx & \\ v=\sqrt{x^2+1} & \end{matrix}\right.\Rightarrow I=\sqrt{x^2+1}.ln(x+\sqrt{x^2+1})-\int dx[/tex]
[tex]\left\{\begin{matrix} u=ln(cosx) & \\ dv=\frac{dx}{cos^2x} & \end{matrix}\right.\Rightarrow \left\{\begin{matrix} du=-\frac{sinx}{cosx}dx=-tanx.dx & \\ v=tanx & \end{matrix}\right.\Rightarrow I=tanx.ln(cosx)+\int tan^{2}xdx=tanx.ln(cosx)+tanx-x+C[/tex]