how can I do the following integration?

Asked May 12 '13 at 05:38

Active May 12 '13 at 06:12

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$$ \int_0^h\!\exp\left( ity + (\alpha-1) \ln y \right)\,dy, $$ where $i = \sqrt{-1}$, $\alpha>0$, and $h>0$.

Please show your work step by step.

I know $$ \int\! \exp \left( mx \right)\,dx = \frac{\exp ( mx )}{m} + c, $$ where $c$ is a constant. So I have done : $$ \int\!\exp\left( ity + (\alpha-1) \ln y\right) dy = \frac{exp \left(ity + (\alpha-1) \ln y\right)}{it + (\alpha-1)\frac{1}{y}} $$ is this right?

Alternative method is not coming in my mind.

edited May 12 '13 at 05:57

Stahl

23,212

asked May 12 '13 at 05:38

time

1,595

6

I think that you would be better received if you took the time to use proper spelling, capitalization, and grammar. – davidlowryduda May 12 '13 at 05:41
1

It is also near impossible as written to tell what you are trying to integrate. – Alex Wertheim May 12 '13 at 05:42
∫(0 to h) exp [ ity + (α-1) ln y ] dy – time May 12 '13 at 05:44
2

@tree, please edit the question to correct typos at least. – Mariano Suárez-Álvarez May 12 '13 at 05:47
@tree What about $t$? – Srijan May 12 '13 at 05:54
@srijan t is a constant . Only the variable is y. – time May 12 '13 at 05:56
@tree do you really want $i$ to be any imaginary number, or do you mean $i = \sqrt{-1}$? – Stahl May 12 '13 at 05:59
@Stahl i = √(-1) – time May 12 '13 at 06:02
@Stahl Thank you very much for reforming my question. Where can i learn LaTex so that i will feel comfortable to join in this site? – time May 12 '13 at 06:05
You might want to simplify the integrand by using some facts about exponentials, e.g., $e^{a+b}=e^ae^b$, $e^{ab}=(e^b)^a$, and $e^{\log a}=a$. – Gerry Myerson May 12 '13 at 06:05
If you check the faq it will direct you to some discussions of LaTeX we've had. – Gerry Myerson May 12 '13 at 06:05
@tree in particular, here is a starting point for formatting some $\LaTeX$. – Stahl May 12 '13 at 06:07

how can I do the following integration?

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