Menu Close

Category: Integration

0-pi-2-cos-x-cos-5-x-sin-x-1-cos-2-x-dx-

Question Number 167328 by cortano1 last updated on 13/Mar/22 $$\:\:\:\:\:\:\int_{\mathrm{0}} ^{\:\pi/\mathrm{2}} \:\frac{\mathrm{cos}\:{x}+\mathrm{cos}\:^{\mathrm{5}} {x}\:\mathrm{sin}\:{x}}{\:\sqrt{\mathrm{1}+\mathrm{cos}\:^{\mathrm{2}} {x}}}\:{dx}\:=? \\ $$ Answered by MJS_new last updated on 13/Mar/22 $$\int\frac{\mathrm{cos}\:{x}\:+\mathrm{cos}^{\mathrm{5}} \:{x}\:\mathrm{sin}\:{x}}{\:\sqrt{\mathrm{1}+\mathrm{cos}^{\mathrm{2}}…

sin-3-x-1-sin-2-x-1-dx-

Question Number 167312 by cortano1 last updated on 12/Mar/22 $$\:\:\:\:\:\:\:\int\:\frac{\mathrm{sin}\:^{\mathrm{3}} \mathrm{x}+\mathrm{1}}{\mathrm{sin}\:^{\mathrm{2}} \mathrm{x}−\mathrm{1}}\:\mathrm{dx}\:=? \\ $$ Commented by Florian last updated on 10/Apr/22 $$\:\:{Simplify}:\:\frac{{sin}^{\mathrm{3}} {x}+\mathrm{1}}{{sin}^{\mathrm{2}} −\mathrm{1}}=\frac{{sin}^{\mathrm{2}} \left({x}\right)−{sin}\left({x}\right)+\mathrm{1}}{{sin}\left({x}\right)−\mathrm{1}}…

NICE-CALCULUS-0-1-ln-1-x-ln-1-x-2-x-dx-

Question Number 167310 by amin96 last updated on 12/Mar/22 $$\boldsymbol{\mathrm{NICE}}\:\boldsymbol{\mathrm{CALCULUS}} \\ $$$$\int_{\mathrm{0}} ^{\mathrm{1}} \frac{\boldsymbol{\mathrm{ln}}\left(\mathrm{1}−\boldsymbol{\mathrm{x}}\right)\boldsymbol{\mathrm{ln}}\left(\mathrm{1}−\frac{\boldsymbol{\mathrm{x}}}{\mathrm{2}}\right)}{\boldsymbol{\mathrm{x}}}\boldsymbol{\mathrm{dx}}=? \\ $$$$ \\ $$$$ \\ $$ Terms of Service Privacy Policy…

Q-2sin-x-3-sin-x-cos-x-dx-

Question Number 167305 by greogoury55 last updated on 12/Mar/22 $$\:\:\:{Q}=\int\:\frac{\mathrm{2sin}\:\left({x}\right)}{\:\sqrt{\mathrm{3}}\:\mathrm{sin}\:\left({x}\right)−\mathrm{cos}\:\left({x}\right)}\:{dx}=? \\ $$ Answered by amin96 last updated on 13/Mar/22 $${Q}=\int\frac{{sin}\left({x}\right)}{\frac{\sqrt{\mathrm{3}}}{\mathrm{2}}{sin}\left({x}\right)−\frac{\mathrm{1}}{\mathrm{2}}{cos}\left({x}\right)}{dx}= \\ $$$$=−\int\frac{{sin}\left({x}\right)}{{sin}\left(\frac{\pi}{\mathrm{6}}−{x}\right)}{dx}\:\:\:\:\:\:\:\:\frac{\pi}{\mathrm{6}}−{x}\:={t} \\ $$$${x}=\frac{\pi}{\mathrm{6}}−{t}\:\:\:\:\:{Q}=\int\frac{{sin}\left(\frac{\pi}{\mathrm{6}}−{t}\right)}{{sin}\left({t}\right)}{dt}= \\…