What is the meaning of Si in the integral of ln(x)cos(x)?

In summary, we can use integration by parts to solve the integral of ln(x).cos(x). This results in the equation ln(x).sin(x) - Si(x) + c, where Si(x) is the integral of sin(x)/x. This can be represented as (2) and can be used to continue solving the integral.
  • #1
leprofece
241
0
integral ln(x).cos(x)
Here I have some clear ideas
U = lnx du = 1/x
dv = cosx so int de cosx = v = -sinx
-sinxlnx -int (sinx)/(x)

Ok I think I must integrate again
u= sinx du = cosx
dv = 1/x v = lnx
Again I got -sinxlnx -int (sinx lnx)
But I am stuck here and I don't know how to finish it??
Can you help me?

Ok i found that integral of sinx/x is Si according to a program but what does Si mean?
 
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  • #2
leprofece said:
integral ln(x).cos(x)
Here I have some clear ideas
U = lnx du = 1/x
dv = cosx so int de cosx = v = -sinx
-sinxlnx -int (sinx)/(x)

Ok I think I must integrate again
u= sinx du = cosx
dv = 1/x v = lnx
Again I got -sinxlnx -int (sinx lnx)
But I am stuck here and I don't know how to finish it??
Can you help me?

Ok i found that integral of sinx/x is Si according to a program but what does Si mean?

Integrating by parts You obtain...

... where...



Kind regards

 

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