Olympiad:Sandbox


 * $$\displaystyle\int \frac{1}{e^x + e^{-x}}\,dx$$
 * $$= \displaystyle\int \frac{1}{e^x + e^{-x}} \frac{e^x}{e^x}\,dx$$
 * $$= \displaystyle\int \frac{e^x}{e^{x^2}+1}\,dx$$
 * $$= \displaystyle\int \frac{1}{u^2 + 1}\,du$$ where $$u = e^x$$
 * $$= \tan^{-1} e^x + C$$