Help With Calc 2 Problems: Integration & Differentiation

[mewmew]

Calc two help please :(

Ok, I have the following two problems:

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

and

$$\int \ \frac{Sin[x]}{1+x^2} \ dx<br />$$

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.

 

[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.

 

[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.

 

[dextercioby]

1. I am not sure why its 0, but that is the form the problem is in. 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.

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.

 

[mewmew]

Thanks a lot!