Chapter 5.9, Problem 4ES

Express the integral in terms of the variable $u$ , but do not evaluate it.

(a) ${\displaystyle {\int }_1^{\sqrt{3}}\frac{\sqrt{{\tan }^{-1}x}}{1+x^2}dx};u={\tan }^{-1}x$

(b) ${\displaystyle {\int }_1^{\sqrt{e}}\frac{dx}{x\sqrt{1-{\left(\ln x\right)}^2}}dx};u=\ln x$