Solving an Integral Without Software: Step-by-Step

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I want you to solve me a following problem without any software and explain me step to step:

int(exp(-x)*sin(a*x)/(x),x=0..infinity);
thenk you
 
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Thread moved to the homework forums. Welcome to the PF, mashjavad. Please tell us what you know already about integration. What learning resources do you have available?
 
Hi mashjavad,

Looks like integration by parts doesn't solve the integral. It takes the form (e^-x sin ax)/x. I used mathematical software to evaluate and obtained exponential integrals with complex numbers in the result. I tink this involves incomplete gamma functions or numerical methods of integration.

Sorry couldn't help much.
 

Thread 'Finding the nth roots of a complex number'

There are two things I don't understand about this problem. First, when finding the nth root of a number, there should in theory be n solutions. However, the formula produces n+1 roots. Here is how. The first root is simply ##\left(r\right)^{\left(\frac{1}{n}\right)}##. Then you multiply this first root by n additional expressions given by the formula, as you go through k=0,1,...n-1. So you end up with n+1 roots, which cannot be correct. Let me illustrate what I mean. For this...
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