Integral of Si(x) and Ci(x)

Here I talked about special functions, and at the end of the post I said I would explain how to integrate these special functions. So here I am, showing you how to integrate the functions Si(x) and Ci(x). If you gave it a try, let me know in the comments if you used this approach!

Integral of Si(x)

U-substitution won’t work, so let’s use integration by parts. We know that Si(x) is given by the integral of sin(x)/x, therefore the derivative of Si(x) is sin(x)/x.

Integral of Ci(x)

For this we are going to use the same procedure.

What do you think the integrals of S(x) and C(x) are? Give it a try and write the answer in the comments!

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