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Category: Integration

1-cot-2-x-1-sin-x-dx-

Question Number 159870 by tounghoungko last updated on 21/Nov/21 $$\:\:\int\:\frac{\mathrm{1}−\mathrm{cot}\:^{\mathrm{2}} {x}}{\mathrm{1}+\mathrm{sin}\:{x}}\:{dx}\:=? \\ $$ Answered by Ar Brandon last updated on 21/Nov/21 $${I}=\int\frac{\mathrm{1}−\mathrm{cot}^{\mathrm{2}} {x}}{\mathrm{1}+\mathrm{sin}{x}}{dx}=\int\frac{\left(\mathrm{1}−\mathrm{cot}^{\mathrm{2}} {x}\right)\left(\mathrm{1}−\mathrm{sin}{x}\right)}{\mathrm{1}−\mathrm{sin}^{\mathrm{2}} {x}}{dx}…

Question-159823

Question Number 159823 by tounghoungko last updated on 21/Nov/21 Answered by Ar Brandon last updated on 21/Nov/21 $${I}=\int_{\mathrm{0}} ^{\mathrm{1}} \frac{\sqrt{\mathrm{1}−{x}}}{\:\sqrt{\mathrm{1}+{x}}}\mathrm{sin}^{−\mathrm{1}} {xdx}=\int_{\mathrm{0}} ^{\mathrm{1}} \frac{\mathrm{1}−{x}}{\:\sqrt{\mathrm{1}−{x}^{\mathrm{2}} }}\mathrm{sin}^{−\mathrm{1}} {xdx}…