1. ## Integration by parts

can someone show the steps to these 2 questions please

integrate (5x^3)/(x^2 +9) dx

integrate x/(x+1) dx

2. #1. Long divide to get: $5\int \frac{x^3}{x^2 + 9} = 5\int \left(x - \frac{9x}{x^2 + 9} \right) \ dx$

Use $u = x^2 + 9$ for that second term.

#2. Add '0' and separate the fractions: $\int \frac{x {\ \color{red}+1 - 1}}{x+1} \ dx \ = \ \ \int \left( 1 - \frac{1}{x+1}\right) \ dx$

(Or use partial fraction decomposition if you're not comfortable with adding the '0')

No integration by parts here!