Anti differentiation using U sub help

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.
  • #1
5
0
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!
 
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  • #2
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).
 
  • #3
Bump up
 
  • #4
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.

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