Rules of Integration:
 kdx  kx  C
 kf ( x)dx  k  f ( x)dx
  f ( x)  g ( x)dx   f ( x)dx   g ( x)dx
1 n 1
x  C n  1 this is call the power rule
n 1
1
1
 x dx   x dx  ln x  C why the absolute value signs? 𝑦 = ln 𝑥 not defined for negative 𝑥.
x
a
n
dx 
x
dx 
1
1 x

2
1 x
a C
ln a
Special case:
e
x
dx  e x  C
dx  arctan x  C
1
1 x2
dx  arcsin x  C
 cos xdx  sin x  C
  sin xdx  cos x  C
 sec xdx  tan x  C
  csc xdx  cot x  C
 sec x tan xdx  sec x  C
  csc x cot xdx  csc x  C
2
2
∫ cosh 𝑥 𝑑𝑥 = sinh 𝑥 + 𝐶
∫ sinh 𝑥 𝑑𝑥 = cosh 𝑥 + 𝐶
Bad news:
1. Integration is harder and more tedious than differentiation
2. To be successful you must be able to differentiate with ease
3. To be successful you must have strong algebra and trigonometry skills
4. There is no chain, quotient or product rule in integration. Integration consists primarily
of pattern recognition and manipulating equations algebraically to put the equation into
a recognizable form
Good news:
1. You can always check your work by differentiating your answer
2. It does become easier with practice