Chapter 8.2, Problem 61E

Integration by Parts State whether you would use integration by parts to evaluate each

integral. If so, identify what you would use for and Explain your reasoning.

a) ${\displaystyle \int \frac{\ln x}{x}dx}$

b) ${\displaystyle \int x\ln xdx}$

c) ${\displaystyle \int x^2{e}^{-3x}dx}$

d) ${\displaystyle \int 2x{e}^{x^2}dx}$

e) ${\displaystyle \int \frac{x}{\sqrt{x+1}}dx}$

f) ${\displaystyle \int \frac{x}{\sqrt{x^2+1}}dx}$