Chapter 8.7, Problem 66E

To determine

The method to find the anti-derivatives of:

(a) ${\displaystyle {\int }_{}^{}\frac{e^x}{e^{2x}+1}dx}$

(b) ${\displaystyle {\int }_{}^{}\frac{e^x}{e^x+1}dx}$

(c) ${\displaystyle {\int }_{}^{}x{e}^{x^2}dx}$

(d) ${\displaystyle {\int }_{}^{}x{e}^{x}dx}$

(e) ${\displaystyle {\int }_{}^{}{e}^{2x}\sqrt{e^{2x}+1}dx}$