Find the integral int_0^1 1/(5+2x-2x^2) (1+e^(2-4x))dx

$$\int_0^1\frac{1}{(5+2x-2x^2)(1+e^{2-4x})}dt$$

Believe me. I tried this sum for a good 1 hour.

Tried Parts. All types of substitution. Almost every known method taught to a student of 12th grader. But in vain. A storke of genious. Thats what i need to solve this.

I took the entire denominator for substituion. Just the polynomial. Just the exponential term. In parts i took just the polynomial. Just the exponential term. Everything. No benefits.

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CompuChip
Homework Helper

And all that while the answer is just
$$\frac{1}{(5+2x-2x^2)(1+e^{2-4x})}$$.

$$dt$$ not $$dx$$. :shy: Foolish to do that to students.

Never expected that from you. Its abvious that its a typing mistake. Its dx.

PS I solved the integral by dirk_mec1. Have a look.

Hey compuchip...

Sorry. I think i was quite arrogant in the last post.

My apologies.

CompuChip
Homework Helper

Hi FedEx,

No need to apologize, my reply wasn't very helpful either
And it's very good that you solved the dirk_mec's integral, although I hope you'll excuse me for not working through the whole calculation :tongue: That I happen to have this label besides my name by no means implies that I know all the answers or I'm good at everything.

As for your question: I did the integration numerically, and it doesn't look particularly nice. In fact I would really see any good way of solving it, which makes sense since you indicated you have tried all common methods already. I wonder if there is a closed form solution...

Hard luck. Theres no solution. I saw this sum on an IIT aspirants website. Unsolved. But i am damn sure that even the toughest of IIT Papers doesnot have a sum like this.