Find the integral of (sin x)/(x)

Alessandra Smith

Alessandra Smith

Answered question

2022-12-14

Find the integral of sinxx.

Answer & Explanation

Greta Mosley

Greta Mosley

Beginner2022-12-15Added 2 answers

Calculate the given function's integral.
Given function: sinxx
The series by Taylor-Maclaurin claims
sinx=x-x33!+x55!-x77!+x99!-x1111!+..............
sinx=n=0(-1)nx2n+1(2n+1)!
So,
sinxxdx=n=0(-1)nx2n+1(2n+1)!xdx
=n=0(-1)nx2n(2n+1)!dx
=n=0(-1)nx2n+1(2n+1)!(2n+1)+c, where C is the integration constant.
Hence, the integral of sinxx is n=0(-1)nx2n+1(2n+1)!(2n+1)+c where C is the integration constant.

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