Two Unintegrated Problems

[adam1111]

How do you integrate sin(X²)
How do you integrate e^-x/(x+1)

[AuSmith]

Are you sure the first is solvable?

On the second, here's a hint,

[unparseable or potentially dangerous latex formula]

[adam1111]

Yes i am sure the first has been solved a college professer did it but he wont tell me the solution :(
The 2nd is just complicated i haven't been able to integrate it I've tried many things
Almost forgot i tried partial fractions for the 2nd one i almost thought i had it but im left with ex or something and i cant get rid of it

[Kurt]

Are they really definite integrals? You can solve for the exact answer (not just a numerical approximation) using a Fresnel integral on the first one, but that requires it to be a definite integral.

[adam1111]

Yes these are definite integrals i beileve the closest i got to the first one was like x^2sin(x^2) through trigonemetric subs. but the 2nd one i tried U subs. and i got to this other integral ln(u)/(1-ln(u)) which is still complicated :cry:

[AuSmith]

I believe "definite integral" means you are integrating on an interval. So, if you could give us some bounds maybe, like from [unparseable or potentially dangerous latex formula] to [unparseable or potentially dangerous latex formula].

I don't think the second one is that hard.

[AuSmith]

As Kurt suggested, a Fresnel integral gives

[unparseable or potentially dangerous latex formula]

where [unparseable or potentially dangerous latex formula].

[unparseable or potentially dangerous latex formula] is an integral that has no closed algebraic representation. But, it's common enough. It's more like [unparseable or potentially dangerous latex formula]

[adam1111]

Im sorry i was mistaken they are INDEFINITE integrals that i am trying to get in the form of transcendental functions the 2nd one is quite more complicated than you think ^^

[AuSmith]

Okay, I see how the second is hard.

If the first is transcendental and can't be expressed with log, exp, and constants, I don't call it solvable. Your probably trying to "solve" it in terms of more popular unsolvable integrals, like erf just a while ago.

[adam1111]

Ive tried many steps to integrating the 2nd one its long and complicated i even tried integration by inspection or asking my self what can i add to make that equal to the original integral. As for the first one i need to find a identity for sin(x^2) to integrate it

[adam1111]

My question on the 2nd one is why can't i do partial fractions A/e^x+B/(x+1) and solve for A and B it seems logical and i dont remember reading a rule in my calculus book that says i can't do that

[AuSmith]

On the first one, Kurt hinted at the Fresnel integral... and I gave an answer. Have you differentiated it to see if it works?

On the second, I thought you meant [unparseable or potentially dangerous latex formula], but I think you mean [unparseable or potentially dangerous latex formula]. You can't do a partial fraction because [unparseable or potentially dangerous latex formula] is not a polynomial. Try combining your two fractions:

[unparseable or potentially dangerous latex formula]

You want to set [unparseable or potentially dangerous latex formula], and since [unparseable or potentially dangerous latex formula] is a variable and [unparseable or potentially dangerous latex formula] are nonzero constants, that doesn't work.