can someone show the steps to these 2 questions please
integrate (5x^3)/(x^2 +9) dx
integrate x/(x+1) dx
#1. Long divide to get: $\displaystyle 5\int \frac{x^3}{x^2 + 9} = 5\int \left(x - \frac{9x}{x^2 + 9} \right) \ dx$
Use $\displaystyle u = x^2 + 9$ for that second term.
#2. Add '0' and separate the fractions: $\displaystyle \int \frac{x {\ \color{red}+1 - 1}}{x+1} \ dx \ = \ \ \int \left( 1 - \frac{1}{x+1}\right) \ dx$
(Or use partial fraction decomposition if you're not comfortable with adding the '0')
No integration by parts here!