Chapter 6.7, Problem 25P

To determine

(a)

To find whether integration by substitution or integration by parts is more appropriate for the below integral

${\displaystyle \int \frac{x^2}{1+x^3}}dx$

To determine

(b)

To find whether integration by substitution or integration by parts is more appropriate for the below integral

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

To determine

(c)

To find whether integration by substitution or integration by parts is more appropriate for the below integral

${\displaystyle \int x^2\ln \left(x^3+1\right)}dx$

To determine

(d)

To find whether integration by substitution or integration by parts is more appropriate for the below integral

${\displaystyle \int \frac{1}{\sqrt{3x+1}}}dx$

To determine

(e)

To find whether integration by substitution or integration by parts is more appropriate for the below integral

${\displaystyle \int x^2\ln x}dx$

To determine

(f)

To find whether integration by substitution or integration by parts is more appropriate for the below integral

${\displaystyle \int \ln x}dx$