- #1
Saladsamurai
- 3,020
- 7
I know this must be similar...
[tex]\int \frac{e^x}{1+e^{2x}}[/tex]
should [tex]u=1+e^{2x}[/tex]?
Casey
[tex]\int \frac{e^x}{1+e^{2x}}[/tex]
should [tex]u=1+e^{2x}[/tex]?
Casey
bob1182006 said:actually this one's a bit trickier.
if you try 1+e^(2x) you won't really go anywhere since the derivative of e^(2x) is 2e^(2x) >< which doesn't appear on the top of the fraction.
So is there any other substitution you can try? one that when derived will give you the quantity that is on top of the fraciton? o.o
I think you mean "what is the derivative of arctan!rocophysics said:yes.
[tex]u=e^{x}[/tex]
[tex]du=e^xdx[/tex]
what is the integral of arctan?
argh! yes actually that would be correct, lol.HallsofIvy said:I think you mean "what is the derivative of arctan!
Another U substitution is a technique used in calculus to simplify integrals involving complex or nested functions. It involves replacing a variable in the integral with a new variable, typically denoted by u, in order to make the integral easier to solve.
"Another U substitution" is useful when you encounter integrals with nested functions or functions that are difficult to integrate. It can also be used when the integral can be rewritten in a more manageable form using a substitution.
To perform "Another U substitution", follow these steps:
Yes, there are some limitations to using "Another U substitution". For example, it may not work for all integrals and can sometimes lead to more complicated integrals. It is important to consider other integration techniques and to practice with different types of integrals to determine when "Another U substitution" is the best approach.
Yes, "Another U substitution" can be used for both indefinite and definite integrals. However, when using it for definite integrals, it is important to adjust the limits of integration accordingly after substituting back in the original variable.