Integration Guide
Fractions
If: num ≥ denom
Divide
If: num < denom
1. Is the derivative of the denominator the numerator?
Ln |denom| + C
2. Can you bring the denominator to the numerator with a negative exponent and can then use
the shortcut?
Shortcut
3. Use partial fractions and ln
Products
1. Do they tell you which method to use?
2. Shortcut
3. Can the product of the derivative of the simpler function and the integral of the more
complex functions be integrated?
Integration by parts
4. Can you replace all the x’s with u’s?
U-subs
Trig
1. Is the integral in the 2nd column of the table?
Integrate by moving from right to left
2. Can you simplify the fraction by writing it in its true form and then integrate?
3. Can you rewrite the integral using trig identities to something you can integrate?
Use trig identities
4. Do you have tan or cot?
Rewrite in fraction form and use ln
5. Do you have sin^2 or cos^2
Rewrite using double angle identity
6. Do you have a product with sin and cos?
Rewrite using product-sum formulae
Fractions
If: num ≥ denom
Divide
If: num < denom
1. Is the derivative of the denominator the numerator?
Ln |denom| + C
2. Can you bring the denominator to the numerator with a negative exponent and can then use
the shortcut?
Shortcut
3. Use partial fractions and ln
Products
1. Do they tell you which method to use?
2. Shortcut
3. Can the product of the derivative of the simpler function and the integral of the more
complex functions be integrated?
Integration by parts
4. Can you replace all the x’s with u’s?
U-subs
Trig
1. Is the integral in the 2nd column of the table?
Integrate by moving from right to left
2. Can you simplify the fraction by writing it in its true form and then integrate?
3. Can you rewrite the integral using trig identities to something you can integrate?
Use trig identities
4. Do you have tan or cot?
Rewrite in fraction form and use ln
5. Do you have sin^2 or cos^2
Rewrite using double angle identity
6. Do you have a product with sin and cos?
Rewrite using product-sum formulae
