# How to integrate Sin(x)/(x)?

by TheDestroyer
Tags: integrate, sinx or x
 P: 1 open your MATLAB and insert the operation then differentiate the answer given by MATLAB then search the solution reverse.... (start from the final step and come to the first step) sometimes the above method will work...but even I am not sure about it
 P: 47 There could be other way as to go for fourier transform keeping f=0 (frequency )in its equation.If h(x)=\hat{f}(x) then  \hat{h}(\xi)= f(-\xi). that is duality of fourier transform.
 P: 2 well.... i looked through all the replies to this question and felt that no one really answered it. sooooo i got the integral to sin(x)/(x) to = -cos(x)(1/2x) + (1/2)ln(x)sin(x) +c done by integration by parts twice. so integral of udv = uv - integral of vdu u = lnx du = 1/x dv = sinx v = -cosx u get -cosx/x + (integral of cosxlnx) ------ do integration by parts again u = lnx du = 1/x dv = cosx v = sinx so u get lnxsinx - (integral of sinx/x). add the (integral of sinx/x) over. So now you have 2(integral of sinx/x) = -cosx/x + lnxsinx divide the 2 over n you get -cos(x)(1/2x) + (1/2)ln(x)sin(x) +c
P: 2
 Quote by Mr.Rabbit87 well.... i looked through all the replies to this question and felt that no one really answered it. sooooo i got the integral to sin(x)/(x) to = -cos(x)(1/2x) + (1/2)ln(x)sin(x) +c done by integration by parts twice. so integral of udv = uv - integral of vdu u = lnx du = 1/x dv = sinx v = -cosx u get -cosx/x + (integral of cosxlnx) ------ do integration by parts again u = lnx du = 1/x dv = cosx v = sinx so u get lnxsinx - (integral of sinx/x). add the (integral of sinx/x) over. So now you have 2(integral of sinx/x) = -cosx/x + lnxsinx divide the 2 over n you get -cos(x)(1/2x) + (1/2)ln(x)sin(x) +c
i lied... i differentiate wrong lol
 P: 1 Essentially you cannot integrate sin(x)/x in general -- you just get something related to the exponential integral which is defined as the integral of e^x/x. However, the integral can be done from -infinity to infinity using coutour integrals in the complex plane. See http://raghumahajan.wordpress.com/20...gral-of-sinxx/ In this case the value of int^infty_infty sin(x)/x is pi.
 HW Helper Thanks P: 4,269 You are trying to find what is called the Sine Integral: http://en.wikipedia.org/wiki/Trigonometric_integral Sine integrals and related functions cannot be represented by elementary functions (they are similar to elliptic integrals in this regard). The value of such functions can be calculated using certain polynomial representations. For example, see Abramowitz and Stegun.

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