Calc BC

When to use Integration by Parts?

Use when there is a complicated integral and u-sub doesn’t work

Acronym for Integration by Parts

How to pick U (UV VDU)

Something that gets simplier when you derive

How to pick V (UV VDU)

Something that you can antiderive

LIPTE Acronym

Logs, Inverse Trig, Polynomials, Trig, Exponentials

Steps for Integration for Parts

1. Find U and DV

2. Write the Integration by Parts Equations

3. Solve

4. (Sometimes you’ll have to do it more than once and or algrebriaclly solve the problem after rewriting the equation)

When to Integrate with Perfect Square

Integrating (Constant/Quadratic)

When to Integrate with Division

Integrating (Polynomial with Greater Degree/Polynomial with Smaller Degree)

When to Integrate with Partial Fraction Decomposistion

Integrating (Linear Function/Polynomial)

Steps for Partial Fraction Decomposistion

Split into A + B over factors. Cross Multiple and Cancel. Plug in x values to find A and B. Integrate

Tropozoidal Sums Formula

A = 1/2(Y1 +Y2) Change in X

Steps for Infinte Limit/Improper Intergals

1. Change into Limit Formula

2. Replace A or B

3. Integrate

4. Solve Definite Integral

5. If real number, converges.

6. If infinity, diverges.

Type: Indefinite

Answer: (2/e)

Type: Indefinite

Answer: 2-2cos(1)

Type: Indefinite

Answer: 1

Type: Indefinite

Answer: -1

Type: Indefinite

Answer: Diverges

Type: Trapozoidal Sums

Answer: 15.4

Type: Trapozoidal Sums

Answer: 91

Type: Indefinite

Answer: 1/16

Type: Indefinite

Answer: Diverges