- #1
e^(i Pi)+1=0
- 247
- 1
Homework Statement
[itex]f(x)=\int\frac{x+1}{x^2+2x}[/itex]
The Attempt at a Solution
I know that this can be solved with substitution. I'm wondering why I get the wrong answer when using this other method...
[itex]f(x)=\int\frac{x+1}{x^2+2x}[/itex]
[itex]=\int\frac{x}{x^2+2x}+\frac{1}{x^2+2x}[/itex]
[itex]=\int\frac{1}{x+2}+\int\frac{1}{x^2+2}[/itex]
[itex]=ln(x+2)+ln(x^2+2) + c[/itex]
I could simplify more, but it's wrong. It should be [itex].5(x^2+2) + c[/itex]
I'm guessing that [itex]\int\frac{1}{x^2+2}\neq ln(x^2+2)[/itex] so in what cases does [itex]\int \frac{1}{x} = ln(x) + c[/itex] not hold?? I just learned this stuff today so any answers will have to be rather explicit please.