Not sure how to do this integral.

**Gotovina7** · April 16th 2008, 04:04 PM

Here she is.

$<br /> \int \frac {1}{x^3}e^\frac{1}{x}<br />$

Thanks.

**Mathstud28** · April 16th 2008, 04:30 PM

Originally Posted by Gotovina7

Here it is.

$\int \frac {1}{x^3}e^\frac{1}{x}$

Thanks.

Using power series rewrite it as $\int\frac{\sum_{n=0}^{\infty}\frac{\bigg(\frac{1}{ x}\bigg)^n}{n!}}{x^3}dx\Rightarrow\int\frac{\sum_{ n=0}^{\infty}\frac{x^{-n}}{n!}}{x^3}dx$

then rewrite it as $\int\sum_{n=0}^{\infty}\frac{x^{-n-3}}{n!}dx$

integrating we get $\int{\frac{e^{\frac{1}{x}}}{x^3}}dx=\sum_{n=0}^{\i nfty}\frac{x^{-n-2}}{(-n-2)n!}$
or you could just use parts whichever way your teacher wants

**mr fantastic** · April 16th 2008, 04:31 PM

Originally Posted by Gotovina7

Here it is.

$\int \frac {1}{x^3}e^\frac{1}{x}$

Thanks.

Make the obvious substitution $u = \frac{1}{x} \Rightarrow dx = -x^2 \, du$ .

Then the integral becomes $\int u e^u \, du$ .

Now use integration by parts.

**Gotovina7** · April 16th 2008, 04:59 PM

Ooh, I got it now! Thanks guys!

**Gotovina7** · April 16th 2008, 05:44 PM

How would I do this one?

$\int \frac{1}{e^x+2 \sqrt{e^x}+1}dx$

Thanks

**Mathstud28** · April 16th 2008, 05:50 PM

Originally Posted by Gotovina7

How would I do this one?

$\int \frac{1}{e^x+2 \sqrt{e^x}+1}dx$

Thanks

Next time start a new post but does this help $\int\frac{1}{e^{x}+2e^{\frac{x}{2}}+1}dx=\int\frac {1}{(e^{\frac{x}{2}}+1)^2}dx$ ?

**mr fantastic** · April 16th 2008, 05:52 PM

Originally Posted by Gotovina7

How would I do this one?

$\int \frac{1}{e^x+2 \sqrt{e^x}+1}dx$

Thanks

Note: New question => New thread.

Make the obvious substitution $u^2 = e^x \Rightarrow 2u \frac{du}{dx} = e^x = u^2 \Rightarrow dx = \frac{2 \, du}{u}$ .

Then the integral becomes (after a little bit of algebra): $2 \int \frac{du}{(u+1)^2 u}$ .

Now use partial fractions etc.

**Gotovina7** · April 16th 2008, 05:55 PM

Ooh, I see it now. Thanks guys. Sorry about the post.

**Jhevon** · April 16th 2008, 06:14 PM

Originally Posted by Gotovina7

Need help with another one, scroll down

please do not delete your question

**Gotovina7** · April 16th 2008, 06:15 PM

Originally Posted by Jhevon

please do not delete your question

Yeah sorry, its back up.

Thread: Not sure how to do this integral.

LinkBack

Thread Tools

Display

Not sure how to do this integral.

Similar Math Help Forum Discussions

Use Cauchy's integral theorem for derivatives to evaluate the contour integral.

Graph the region of integration and evaluate the double integral (integral from 0 to

Explaining result: comparing line integral and two-form integral

write [integral of] dx/SQRT(sinx) in terms of an elliptic integral

Evaluating a double integral to find its signle integral.

Search Tags