Anti differentiation using U sub help

[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!

 

[HallsofIvy]

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).

 

[Jishent]

Bump up

 

[Jishent]

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