Question Number 102701 by 175mohamed last updated on 10/Jul/20

Evaluate:  ∫((sin x)/x)dx

Commented by M±th+et+s last updated on 10/Jul/20

go to Q.98713 i solved this question

Answered by PRITHWISH SEN 2 last updated on 10/Jul/20

∫(1/x){x−(x^3 /(3!)) +(x^5 /(5!))−...}dx  = Σ_(r=1) ^∞ (−1)^(r+1) (x^(2r−1) /((2r−1).(2r−1)!))  please check.

Answered by mathmax by abdo last updated on 10/Jul/20

at form of serie  wehave sinx =Σ_(n=0) ^∞  (((−1)^n  x^(2n+1) )/((2n+1)!))  with radius r=+∞  ⇒((sinx)/x) =Σ_(n=0) ^∞  (((−1)^n  x^(2n) )/((2n+1)!)) ⇒ ∫ ((sinx)/x)dx =Σ_(n=0) ^∞  (((−1)^n )/((2n+1)!)) ∫ x^(2n)  dx  =Σ_(n=0) ^∞  (((−1)^n )/((2n+1)!(2n+1)))x^(2n+1)  +C