Question Number 86091 by jagoll last updated on 27/Mar/20
$$\int\:\frac{\mathrm{sin}\:\mathrm{x}−\mathrm{cos}\:\mathrm{x}}{\:\sqrt{\mathrm{sin}\:\mathrm{2x}}}\:\mathrm{dx} \\ $$
Commented by john santu last updated on 27/Mar/20
$${in}\:{other}\:{way} \\ $$$$\int\:−\frac{{d}\left(\mathrm{sin}\:{x}+\mathrm{cos}\:{x}\right)}{\:\sqrt{\left(\mathrm{sin}\:{x}+\mathrm{cos}\:{x}\right)^{\mathrm{2}} −\mathrm{1}}}\: \\ $$$$−\int\:\frac{{du}}{\:\sqrt{{u}^{\mathrm{2}} −\mathrm{1}}}\:=\:−\mathrm{ln}\mid{u}+\sqrt{{u}^{\mathrm{2}} −\mathrm{1}}\:\mid\:+\:{c} \\ $$$$=\:−\:\mathrm{ln}\:\mid\mathrm{sin}\:{x}+\mathrm{cos}\:{x}+\sqrt{\mathrm{sin}\:\mathrm{2}{x}}\:\mid\:+{c} \\ $$
Answered by jagoll last updated on 27/Mar/20
Commented by john santu last updated on 27/Mar/20
$${great} \\ $$