# Thread: Need help integrating improper integral

Hello,

Thanks,

2. ## Re: Need help integrating improper integral

Originally Posted by l flipboi l
Hello,

Thanks,
Are you meant to be integrating wrt n? If so, reverse the order of the summation and the integral, using an appropriate theorem to justify this, and then integrate. There is an obvious substitution to make.

3. ## Re: Need help integrating improper integral

Originally Posted by l flipboi l
Hello,

Thanks,
I don't see an integral...

4. ## Re: Need help integrating improper integral

Oops sorry, it should be [1,t) e^(1/x^7)/x^8

Not sure how to do this...

5. ## Re: Need help integrating improper integral

Originally Posted by l flipboi l
Oops sorry, it should be [1,t) e^(1/x^7)/x^8

Not sure how to do this...
Assuming you mean $\displaystyle \displaystyle \int_1^t{\frac{e^{\frac{1}{x^7}}}{x^8}\,dx} = -\frac{1}{7}\int_1^t{e^{\frac{1}{x^7}}\left(-\frac{7}{x^8}\right)\,dx}$, make the substitution $\displaystyle \displaystyle u = \frac{1}{x^7} \implies du = -\frac{7}{x^8}\,dx$ and make note that $\displaystyle \displaystyle u(1) = 1$ and $\displaystyle \displaystyle u(t) = \frac{1}{t^7}$.