Question Number 67359 by mhmd last updated on 26/Aug/19
$$\int{siny}/{y}\:\:{dy} \\ $$
Commented by mathmax by abdo last updated on 26/Aug/19
$${at}\:{form}\:{of}\:{serie}\:\:{we}\:{have}\:{siny}\:=\sum_{{n}=\mathrm{0}} ^{\infty} \:\frac{\left(−\mathrm{1}\right)^{{n}} {y}^{\mathrm{2}{n}+\mathrm{1}} }{\left(\mathrm{2}{n}+\mathrm{1}\right)!}\:\Rightarrow \\ $$$$\frac{{siny}}{{y}}\:=\sum_{{n}=\mathrm{0}} ^{\infty} \:\frac{\left(−\mathrm{1}\right)^{{n}} {y}^{\mathrm{2}{n}} }{\left(\mathrm{2}{n}+\mathrm{1}\right)!}\:\Rightarrow\:\int\:\frac{{siny}}{{y}}{dy}\:=\sum_{{n}=\mathrm{0}} ^{\infty} \:\frac{\left(−\mathrm{1}\right)^{{n}} }{\left(\mathrm{2}{n}+\mathrm{1}\right)!\left(\mathrm{2}{n}+\mathrm{1}\right)}{y}^{\mathrm{2}{n}+\mathrm{1}} \:+{c} \\ $$
Answered by Joel122 last updated on 26/Aug/19
$$\mathrm{Si}\left({x}\right)\:+\:{C} \\ $$