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Category: Integration

0-pi-2-1-sec-2-t-sec-t-1-sec-t-2-2-dt-

Question Number 136969 by liberty last updated on 28/Mar/21 $$\int_{\mathrm{0}} ^{\:\pi/\mathrm{2}} \frac{\left(\mathrm{1}+\mathrm{sec}\:^{\mathrm{2}} \mathrm{t}\right)\:\sqrt{\mathrm{sec}\:\mathrm{t}}}{\left(\mathrm{1}+\mathrm{sec}\:\mathrm{t}\right)^{\mathrm{2}} −\mathrm{2}}\:\mathrm{dt}\:=?\: \\ $$ Answered by EDWIN88 last updated on 28/Mar/21 $$\:\mathrm{E}\:=\:\int_{\mathrm{0}} ^{\:\pi/\mathrm{2}}…

csc-4-x-cot-2-x-dx-

Question Number 136971 by Eric002 last updated on 28/Mar/21 $$\int{csc}^{\mathrm{4}} \left({x}\right)\:{cot}^{\mathrm{2}} \left({x}\right)\:{dx} \\ $$ Answered by Ñï= last updated on 28/Mar/21 $$\int{csc}\:^{\mathrm{4}} {x}\mathrm{cot}\:^{\mathrm{2}} {xdx}=−\int\left(\mathrm{1}+\mathrm{cot}\:^{\mathrm{2}} {x}\right)\mathrm{cot}\:^{\mathrm{2}}…

4-x-2-x-dx-

Question Number 136948 by leena12345 last updated on 28/Mar/21 $$\int\frac{\sqrt{\mathrm{4}+{x}^{\mathrm{2}} }}{{x}}{dx} \\ $$ Answered by Olaf last updated on 28/Mar/21 $$\mathrm{F}\left({x}\right)\:=\:\int\frac{\sqrt{\mathrm{4}+{x}^{\mathrm{2}} }}{{x}}\:{dx} \\ $$$$\mathrm{F}\left({u}\right)\:\overset{{x}=\mathrm{2sh}{u}} {=}\:\:\:\:\int\frac{\sqrt{\mathrm{4}+\mathrm{4sh}^{\mathrm{2}}…

cos-x-e-cos-x-sin-x-dx-

Question Number 136935 by metamorfose last updated on 27/Mar/21 $$\int{cos}\left({x}\right){e}^{{cos}\left({x}\right)+{sin}\left({x}\right)} {dx}=…? \\ $$ Answered by liberty last updated on 27/Mar/21 $$\int\:\mathrm{cos}\:\mathrm{x}.\mathrm{e}^{\mathrm{cos}\:\mathrm{x}} .\mathrm{e}^{\mathrm{sin}\:\mathrm{x}} \:\mathrm{dx}\:= \\ $$$$\mathrm{by}\:\mathrm{parts}…

e-ln-sin-1-x-1-x-2-dx-

Question Number 136929 by liberty last updated on 27/Mar/21 $$\int\:\frac{\mathrm{e}^{\mathrm{ln}\:\left(\mathrm{sin}^{−\mathrm{1}} \mathrm{x}\right)} }{\:\sqrt{\mathrm{1}−\mathrm{x}^{\mathrm{2}} }}\:\mathrm{dx}\:=\:?\: \\ $$ Answered by Dwaipayan Shikari last updated on 27/Mar/21 $$\int\frac{{e}^{{log}\left({sin}^{−\mathrm{1}} {x}\right)}…