Calculate: ∫e^x * square root(1-x^2) dx?

Question

I tried using substitution x=sin t , and partial integration.

Northstar - The first one, I also tried to calculate it in Wolfram's Mathematica and didn't get anything, but a friend assures me that he got this integral at a math test. He gave to me and I have been tormenting with it for days now :(

Answer 1

Your formula is a little ambiguous. Do you mean:

∫(e^x)*√(1 - x²) dx

or

∫(e^[x√(1 - x²)] dx

I tried both ways with the Wolfram integrator and got no results. Here is a link.

http://integrals.wolfram.com/index.jsp

Either way, I don't think this has a solution in closed form.

Answer 2

dont use any substitution for this learn by parts method to do this for now i'll give a lil information for that ∫u.v dx! = u∫vdx-∫(d-dx(u)∫vdx)dx .. u and v can choose using ilate .... i= inverse
l=log ..a=algebra....t=trignometric.... e= exponetial function