Try the Free Math Solver or Scroll down to Tutorials!

 Depdendent Variable

 Number of equations to solve: 23456789
 Equ. #1:
 Equ. #2:

 Equ. #3:

 Equ. #4:

 Equ. #5:

 Equ. #6:

 Equ. #7:

 Equ. #8:

 Equ. #9:

 Solve for:

 Dependent Variable

 Number of inequalities to solve: 23456789
 Ineq. #1:
 Ineq. #2:

 Ineq. #3:

 Ineq. #4:

 Ineq. #5:

 Ineq. #6:

 Ineq. #7:

 Ineq. #8:

 Ineq. #9:

 Solve for:

 Please use this form if you would like to have this math solver on your website, free of charge. Name: Email: Your Website: Msg:

# Review of Techniques of Integration

Strategy

• Identify the type of integral you have.

• Try using the simplest technique for your integral.

• If that doesn’t work, try the next-level method
(might involve more work, but is more likely to
work).

• You may have to break-up the integral into several
parts and use a different method for each
part.

u-Substitution

Goal:
Reduce the integral to one of the 10 basic
integrals in the table.

Works:
If the integrand is nice enough to have exactly
the chain rule form:  Examples: Integration by parts

Goal:
Figure out the integral of a product of two functions
(polynomials, exponentials, logs, trig, inverse
trig, etc).

Works: For all the times when u-substitution fails

Notes:
Needed for (Use Trig-Tricks for
most other trig integrals)

Examples: Trig Tricks

Goal: Integrals of combinations of trig functions
Examples: The 4 steps

Check these steps (in order!) to simplify your integral
as much as needed:

1: If you have an integral of a product of
trig functions with different angles (Ex: 3x ≠
4x) you MUST use trig identities to break it
up into a sum of different terms before you can
make any progress: 2: If one is odd, u = other This gives the right
u-substitution for integrals
(with positive or zero powers). You will also
need to use cos2 x + sin2 x = 1.. Example: then , so u = sin x and
use cos2 x = 1 − u2 to get 3: If both powers are even,
then you need to use the half-angle formulas: 4: SET TOS Use sec2 x = 1 + tan2 x with
SET: TOS: Ex: Square roots

• If you have a then let u = so
u2 = ax+b and 2u du = a dx and x = (u2−b)/a
• If you have a then • If you have a then • If you have a then • If you have a then First,
complete the square, then let
u = x−d and
look again, example: • These work with positive or negative powers of

Rational Functions

 “Rational fcn” means polynomial polynomial  : Complete the square and use
square roots guide. Everything else needs Partial Fractions:

1. NO Improper fractions: Convert .
You MUST do this first! (Use long division or
synthetic division)

2. Factor numerator, denominator, cancel stuff

3. Expand out as a sum of partial fractions (each
will be one of the “easy ones”)