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Hi! I'd love this question. I'll try using Integration by parts.

Differentiate:

---

Now,

Simplify the integral

Substitute back:

So the final answer:

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Where did you find this question?

You left the dx. This is where you got wrong because now if you are integrating with u/v, you should also change the dx to anything like du or dv. Can you please tell me the complete question?

Let, u = g(x)

Differentiate both sides with respect to x:

Now sub. back in the integral:

This is the simplest to what I know. If you give me the original equation, I might help you solving it.

Ok that's strange and I had never seen such thing before

Hey dude, I calculated 100s of values and the final approximate answer was 0 as shown in the figure. You can see the complete execution at https://ktesla.infy.uk/math.html But only open if you are on a PC as this has various nested loops that might hang your computer a bit (3 GB RAM)

Thanks Bob!

I'll definitely love that.

Tomorrow I have exam of Optional Mathematics and I'll ask my teacher about the question. Maybe he can help.

Ok now I don't seek any way to prove the equation. I tried dozens of methods and the only thing I can say is -- This cant be proved using pure algebra. I may be wrong but I'll be still good if we get any solution.

I am in class 10 and I've started learning calculus (class 11) and after some time, when I'll find myself ready, I'll try learning Taylor Series and the Reimann zeta function. once I had a question something like

. I couldn't solve this and when I asked someone about it, they replied that this was a non elementary function an is written as Ei(x). That time I first saw Gamma and Zeta function.