can someone solve int(e^x/(cos(x)))

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can someone solve int(e^x/(cos(x)))

Mathematics
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Are you familiar with integration by parts?
yes ... but i am not able to solve using that ...
\[\int\limits_{?}^{?} udv = uv - \int\limits_{?}^{?} vdu\] What should we choose as our u and dv?

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may be v=e^x and u=cos(x)
Sure. Carry out integration by parts once. What do you end up with? (You should have an integral remaining on the right hand side that seems just as difficult to solve as this one. Leave it be for now)
Still there? You should end up with \[\int\limits\limits_{?}^{?}e ^{x}\cos x = e ^{x}\sin x - \int\limits\limits_{?}^{?}e ^{x}\sin x\] You would then perform integration by parts on the last term again, which will give you: \[\int\limits\limits_{?}^{?}e ^{x}\cos x = e ^{x}\sin x - (-e ^{x}\cos x + \int\limits_{?}^{?}e ^{x}\cos x )\] Distribute the negateive, and move the integral term to the right hand side. Divide both sides by 2.
I thought he was trying to integrate \[\int\limits_{}e^x/cosx dx\]
...Guess that'll teach me to read the problem carefully. One moment to do the correct work.
the problem is \[\int{\frac{e^x}{\cos{x}}}\]
The actual problem I have is little more complex \[\int{\frac{e^{ax}}{\sqrt{b+c\cos{dx}}}}\]
is the dx in the square root?
I am sorry ... \[\int{\frac{e^{ax}}{\sqrt{b+c\cos{(x)}}}dx}\]
What level of math is this for? I'm having difficulty finding a way to make this clean...
I am working here to solve an model and got struck with this equation. It should be level of some master's engineering course.
Well, I went ahead and used some software to examine the two deceptively simple looking integrals. The answer to the first involves a hypergeometric function, and it couldn't solve the second. Sorry, I don't think I'll be of much use to you on this.
Well.... thats explains why I'm stummped
\[\int\limits_{a}^{b}e^x/\cos x\] let u=e^x, du=e^x dx, dx=du/e^x so you have \[\int\limits_{a}^{b}du/cosx =\int\limits_{a}^{b} \sec x = \int\limits_{a}^{b}\ln \sec x + \tan x + C\] Hope this helps
you cant do that because you have du/x, which means you have the change in u=du over cos(x), it has to either has to be du/u or dx/x or in the case of trig substitution dtheta/theta....... because of that your final answer lacks e^x and doesn't make sense

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