# Anti differentiation using U sub help

• Jishent
In summary, the conversation is about a student studying for their AP Calc exam and needing help with integration problems involving different functions such as e^x, x^2, and ln x. They discuss setting different variables and using u-substitution to solve the problems. The conversation also includes a question about a more complex problem involving multiple functions.

#### Jishent

I am self studying for my AP Calc exam. I have just started on integration and I need a few pointers for a few questions. So here it is...

y= (e^x)/(1+(e^x)^2)

So I set u=e^x
du=e^x

then I am stuck.

the second question is (btw [{( are all used as parentheses to make it abit less confusing)

y=(x^2)/[{(x^3)+1)}^12]
I setted u=(x^3)+1
du=3x^2
(1/3)du = (x^2)dx
(1/3)integral sign [1/(u^12)]du
stuck there after

and 3

y=[(lnx)^3]/x

do i set x as u? or lnx?

Last of all I have no clue on number 4 which is

y=sin(2x)*e^[cos(2x)]

Many thanks!

Jishent said:
I am self studying for my AP Calc exam. I have just started on integration and I need a few pointers for a few questions. So here it is...

y= (e^x)/(1+(e^x)^2)

So I set u=e^x
du=e^x

then I am stuck.
Try u= 1+ (e^x)^2

the second question is (btw [{( are all used as parentheses to make it abit less confusing)

y=(x^2)/[{(x^3)+1)}^12]
I setted u=(x^3)+1
du=3x^2
(1/3)du = (x^2)dx
(1/3)integral sign [1/(u^12)]du
stuck there after
1/u^12= u^(-12). Integrate that.

and 3

y=[(lnx)^3]/x

do i set x as u? or lnx?
It should be obvious that "u= x" does not help- it just replaces the letter x with the letter u! So try u= ln x.

Last of all I have no clue on number 4 which is

y=sin(2x)*e^[cos(2x)]

Many thanks!
Try u= cos(2x).

Bump up

Finished with all of them...unsure about number 1. Ended up with arctan*e^x +c

## 1. What is anti differentiation?

Anti differentiation, also known as integration, is the process of finding the original function from its derivative. It is the inverse operation of differentiation.

## 2. What is U sub?

U sub, also known as the substitution method, is a technique used in integration to simplify the integration of complex functions. It involves substituting a variable with a simpler expression in order to make the integration more manageable.

## 3. How do I know when to use U sub?

U sub is most commonly used when integrating a function that involves a product of two functions or a function within a function. It can also be used when integrating trigonometric functions or rational functions.

## 4. What is the general process for anti differentiation using U sub?

The general process for anti differentiation using U sub involves identifying a function that can be substituted with a simpler expression, making the substitution, and then applying the integration rules to solve the resulting integral.

## 5. How can I practice and improve my skills in anti differentiation using U sub?

The best way to practice and improve your skills in anti differentiation using U sub is to work through a variety of practice problems and exercises. You can also watch tutorials, attend workshops, or seek help from a tutor or teacher to further enhance your understanding of the concept.