A Hybrid Parametric Area with d(theta) (10-R p.747 #57)

 A Hybrid Parametric Area with d(theta) (10-R p.747 #57)

A Bounded Area (def Int) with log base 4 (5.5 p359 #81)

 A Bounded Area (def Int) with log base 4 (5.5 p359 #81)

This one has u substitution a a conversion from base 4 to bas e, confirming with the TI-84

An Indefinite Integral with Exponents (5.5 p 359 #76)

 An Indefinite Integral with Exponents (5.5 p 359 #76)

This includes u-substitution, and an exponential function in base 2

The Area of a Region That Involves a Secant Function (5.2 p331 #71)

 The Area of a Region That Involves a Secant Function (5.2 p331 #71)

Another Definite Integral without u-Substitution (5.2 p 331 #65)

 Another Definite Integral without u-Substitution (5.2 p 331 #65)

A Definite Integral Requiring u-Substitution (5.2 p 330 #51)

 A Definite Integral Requiring u-Substitution (5.2 p 330 #51)

Another Slope Field and Differential Equation with Natural Logs (5-2 p330 #50)

 Another  Slope Field and Differential Equation with Natural Logs (5-2 p330 #50)

Slope Fields and Differential Equations with Natural Logs (5-2 p330 #49)

 Slope Fields and Differential Equations with Natural Logs (5-2 p330 #49)

A slope field and a diffyQ checked with the TI-84

A u-Sub Involving Natural Log ln x (5-2 p330 #49)

 A u-Sub Involving Natural Log ln x (5-2 p330 #49)

Long Division AND u-Substitution help this Integral (5-2 p330 #21)

 Long Division AND u-Substitution help this Integral (5-2 p330 #21)

Long Division Before Integrating (5-2 p330 #17)

Long Division Before Integrating (5-2 p330 #17)

This one looks like a difficult u-sub, but turns out to be easy after long division!

U-substitution with a Definite Integral (4-R p310 #67)

 U-substitution with a Definite Integral (4-R p310 #67)

When you use u-substitution with a definite integral, you don't have to switch back to make an expression in terms of x.  Since any definite integral is the signed area, it is just a number.  After finding the anti-derivative in terms of you, the FTC can be used to arrive at the answer. 

Using the u-substitution Technique with an Indefinite Integral (4-R p301 #59)

 Using the u-substitution Technique with an Indefinite Integral (4-R p301 #59)

A basic example of how to integrate something that looks like a product, where one factor has something in common with the derivative of the other factor.

Some Complicated Integrals That Are Easier than they Appear! (4-5 p 307 #81)

 4-5 p 307 #81  Some Complicated Integrals That Are Easier than they Appear!

4-5 p 307 #81  Some Complicated Integrals That Are Easier than they Appear!  U-substitution to the rescue!

Some Basic Antiderivatives (4.1 p. 255 27, 31, 33)

 Some Basic Antiderivatives (4.1 p. 255 27, 31, 33)

Some antiderivatives for beginners. Don't forget there is usually a nice table of anti derivatives on the inside cover of your textbook.  These are General solutions we add a C (for an arbitrary constant) to describe all the functions that have the integrand as a derivative.