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Category: Integration

cos-2x-3-cos-x-dx-

Question Number 88586 by M±th+et£s last updated on 11/Apr/20 $$\int\frac{\sqrt{{cos}\left(\mathrm{2}{x}\right)+\mathrm{3}}}{{cos}\left({x}\right)}{dx} \\ $$ Answered by TANMAY PANACEA. last updated on 11/Apr/20 $$\int\frac{{cos}\mathrm{2}{x}+\mathrm{3}}{{cosx}\sqrt{\mathrm{3}+{cos}\mathrm{2}{x}}}{dx} \\ $$$$\int\frac{\mathrm{2}{cos}^{\mathrm{2}} {x}+\mathrm{2}}{{cosx}\sqrt{\mathrm{2}{cos}^{\mathrm{2}} {x}+\mathrm{2}}}…

0-pi-2-ln-2-1-sin-t-1-sin-t-dt-

Question Number 154080 by iloveisrael last updated on 14/Sep/21 $$\:\:\:\:\Omega\:=\int_{\mathrm{0}} ^{\:\frac{\pi}{\mathrm{2}}} \mathrm{ln}\:^{\mathrm{2}} \left(\frac{\mathrm{1}+\mathrm{sin}\:{t}}{\mathrm{1}−\mathrm{sin}\:{t}}\right){dt} \\ $$ Answered by mindispower last updated on 14/Sep/21 $$=\int_{\mathrm{0}} ^{\frac{\pi}{\mathrm{2}}} \mathrm{4}{ln}^{\mathrm{2}}…

prove-for-0-lt-a-lt-2-0-x-a-1-dx-1-x-x-2-2pi-3-cos-2pia-pi-6-cosec-pia-

Question Number 88547 by ajfour last updated on 11/Apr/20 $${prove}\:{for}\:\left(\mathrm{0}<{a}<\mathrm{2}\right) \\ $$$$\int_{\mathrm{0}} ^{\:\infty} \frac{{x}^{{a}−\mathrm{1}} {dx}}{\mathrm{1}+{x}+{x}^{\mathrm{2}} }\:=\:\frac{\mathrm{2}\pi}{\:\sqrt{\mathrm{3}}}\mathrm{cos}\:\left(\frac{\mathrm{2}\pi{a}+\pi}{\mathrm{6}}\right)\mathrm{cosec}\:\pi{a}\:. \\ $$ Answered by mind is power last updated…