Q.Evaluate $\displaystyle\int \frac{1}{x^{2}-25}\,dx$.

This chapter's toolkit is five standard-formula integrals: $\int x^{n}dx=\frac{x^{n+1}}{n+1}+C$ ($n\ne-1$), $\int\frac{1}{x}dx=\ln|x|+C$, $\int e^{x}dx=e^{x}+C$, $\int\frac{1}{x^{2}-a^{2}}dx=\frac{1}{2a}\ln\left|\frac{x-a}{x+a}\right|+C$ ($x>a$), and $\int\frac{1}{a^{2}-x^{2}}dx=\frac{1}{2a}\ln\left|\frac{a+x}{a-x}\right|+C$ ($a>x$). Combined with the linearity of integration (a sum integrates term by term, and constants pull outsid …