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Anti differentiation using U sub help

  • Thread starter Jishent
  • Start date
  • #1
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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!
 

Answers and Replies

  • #2
HallsofIvy
Science Advisor
Homework Helper
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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
5
0
Bump up
 
  • #4
5
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Finished with all of them...unsure about number 1. Ended up with arctan*e^x +c
 

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