# Thread: I could not solve this integral

1. ## I could not solve this integral

hello every body
i wondering if any one can help me with this integral

thank you

2. ## Re: I could not solve this integral

Assuming $a \neq 0$, rewrite it as

\begin{align*} \displaystyle S &= \sum \limits_{k=0}^\infty~\left(\int_{\frac{k \pi}{a}}^{\frac{(k+1)\pi}{a}}~(-1)^k e^{-\beta x}\sin(a x)~dx\right) \\ \\ &=\sum \limits_{k=0}^\infty~(-1)^k\left(\int_{\frac{k \pi}{a}}^{\frac{(k+1)\pi}{a}}~e^{-\beta x}\sin(a x)~dx\right)\\ \\ &=\sum \limits_{k=0}^\infty~(-1)^k \left(\dfrac{\left(e^{\frac{\pi \beta }{a}}+1\right) e^{-\frac{\pi \beta (k+1)}{a}} (a \cos (\pi k)+\beta \sin (\pi k))}{a^2+\beta ^2}\right) \\ \\ &= \dfrac{a \left(e^{\frac{\pi \beta }{a}}+1\right)}{\left(e^{\frac{\pi \beta }{a}}-1\right) \left(a^2+\beta ^2\right)} \end{align*}

3. ## Re: I could not solve this integral

thank you so much for your help!!
I have been following the same path to solve it. and I asking if there are no a negative signe missed since the 3 ligne

4. ## Re: I could not solve this integral

Originally Posted by nicekiller231
and I asking if there are no a negative signe missed since the 3 ligne
I don't understand what you are saying.