Things You Need to Know

• ( f '(x) / f(x) ) dx = ln|f(x)| + C
• (d/dx)(tan^-1(x)) = 1/(1+x²)  so 1/(1+x²) dx = tan^-1(x) + C

• e^a+b = e^ae^b
• e^ab = (e^a )^b
  
• ln(a/b) = ln(a)-ln(b)
• ln(ab) = ln(a)+ln(b)
• ln(a^r ) = r ln(a)
• e^ln(x) = x  and ln(e^x) = x for all real values of x for which both sides are defined
  
• ln(a+b) usually doesn't break up
• e^a+b = e^a + e^b Wrong!

• Integration by parts:  udv = uv - vdu;   pick u so that du is easier to deal with and v isn't much worse than dv.