I'm looking for examples of integration that use this method

[Ryuk1990]

My professor is teaching us to use integration by finding the derivative of a function. I think he calls this technique the product rule or reverse chain rule.

For example, integrate sin(4x) dx. I find the derivative of the inner function which is 4 and I even it out by multiplying the whole package by 1/4. The integral of sin is -cos so it's -1/4cos4x.

This is a very simple example and I'm looking for websites that show much harder examples that use this technique. The problem is that most calculus tutorial sites seem to use u-subs or integration by parts to show how to do the more complicated examples.

 

[lavinia]

not sure what you want here. Why not try using integraption by parts to derive the Taylor series for a function.

 

[Mark44]

My professor is teaching us to use integration by finding the derivative of a function. I think he calls this technique the product rule or reverse chain rule.

You are confusing two different techiques here. Integration by parts is the reverse of the product rule in differentiation. Integration by substitution is the reverse of the chain rule in differentiation.

For example, integrate sin(4x) dx. I find the derivative of the inner function which is 4 and I even it out by multiplying the whole package by 1/4. The integral of sin is -cos so it's -1/4cos4x.

This is a very simple example and I'm looking for websites that show much harder examples that use this technique. The problem is that most calculus tutorial sites seem to use u-subs or integration by parts to show how to do the more complicated examples.

Your calculus textbook should have numerous examples of ordinary substitution (what you are calling u-sub).

 

[Feldoh]

My professor is teaching us to use integration by finding the derivative of a function. I think he calls this technique the product rule or reverse chain rule.

For example, integrate sin(4x) dx. I find the derivative of the inner function which is 4 and I even it out by multiplying the whole package by 1/4. The integral of sin is -cos so it's -1/4cos4x.

This is a very simple example and I'm looking for websites that show much harder examples that use this technique. The problem is that most calculus tutorial sites seem to use u-subs or integration by parts to show how to do the more complicated examples.

What you are describing IS a u-substitution.

sin(4x)dx

let u=4x which means du = 4dx => 1/4du = dx

 

[Ryuk1990]

Ah well I suppose it's the notation of the u-subbing that confuses me. I like the intuitive shortcut of the method which is what my teacher shows us.

 

[mynameisfunk]

Thats something most people can develop after doing LOTS of u-substitution problems. I know I did. After a while you just see it and your u-substituting becomes an 'intuitive shortcut method'. If you want to understand it, learn both ways.