(adsbygoogle = window.adsbygoogle || []).push({}); 1. The problem statement, all variables and given/known data

Calculate the following integral exactly (no approximations) by the method of integration by parts:

∫_{0}^{t}SinIntegral[x]dx

2. Relevant equations

the following hints are given:

D[SinIntegral[x], x] = Sinc[x]; and

SinIntegral[0] = 0

3. The attempt at a solution

The integration by parts forrmula is ∫_{a}^{b}u[x]v^{'}[x]dx = u[x]v[x]|_{a}^{b}-∫_{a}^{b}v[x]u^{'}[x]dx.

The problem I have is that whether I let u[x]=1 and v'[x]= SinIntegral[x], or u[x]=SinIntegral[x] and v'[x]= 1, either way the integral on the right is more complex than what I started with (either ∫_{0}^{t}xSinc[x]; or ∫_{0}^{t}SinIntegral[x].

Any help is appreciated. I hope all the programming tags work here, otherwise this will look like a mess. It may still look like a mess

So it seems to me that, although the question requires the differentiation by parts method, such method does not work because it you get more complicated integrals

1. The problem statement, all variables and given/known data

2. Relevant equations

3. The attempt at a solution

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# Homework Help: Integration by parts SinIntegral[x]

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