Homework Help: Calc two help please

1. Feb 8, 2005

mewmew

Ok, I have the following two problems:

$$\frac{d}{dx} \ \int_0^1 \ e^{tan^-1(t)} \ dt \\\\$$

and

$$\int \ \frac{Sin[x]}{1+x^2} \ dx$$

I have tried to do substitution on both and integration by parts on the second one but nothing seems to work. If I could just get some pointers in the right direction on where to start that would be awesome, thanks a lot.

Last edited: Feb 8, 2005
2. Feb 8, 2005

dextercioby

1.Are you sure about the first...?In the form posted,it's zero...
2.It's not an integral solvable in the "family" of "elementary"functions.

Daniel.

3. Feb 8, 2005

mewmew

1. I am not sure why its 0, but that is the form the problem is in and 0 is what I got when I did it in Mathematica. I am not really sure on how to go about evaluating it though as if I do U substitution I get x in my denominator.

2.If it makes any difference it is actually an definite integral with lower limit -1 and upper limit 1. I don't think that should make a difference however.

Thanks for the help.

Last edited: Feb 8, 2005
4. Feb 8, 2005

dextercioby

OMG,for #2,it MAKES A HUGE DIFFERENCE...The integral is zero for symmetry reasons...

1.the first integral,in the form u posted is a number.The derivative of a number wrt any variable (x,y,z,t,...) is IDENTICALLY ZERO.

Daniel.

5. Feb 8, 2005

mewmew

Thanks a lot!