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Category: Integration

J-dx-1-tan-x-csc-x-cot-x-sec-x-

Question Number 134058 by john_santu last updated on 27/Feb/21 $$\mathcal{J}\:=\:\int\:\frac{{dx}}{\mathrm{1}+\mathrm{tan}\:{x}+\mathrm{csc}\:{x}+\mathrm{cot}\:{x}+\mathrm{sec}\:{x}} \\ $$ Answered by john_santu last updated on 27/Feb/21 $$\mathcal{J}=\int\:\frac{{dx}}{\mathrm{1}+\frac{\mathrm{sin}\:{x}}{\mathrm{cos}\:{x}}+\frac{\mathrm{1}}{\mathrm{sin}\:{x}}+\frac{\mathrm{cos}\:{x}}{\mathrm{sin}\:{x}}+\frac{\mathrm{1}}{\mathrm{cos}\:{x}}} \\ $$$$\:=\:\int\:\frac{\mathrm{cos}\:{x}\:\mathrm{sin}\:{x}}{\mathrm{sin}\:{x}\mathrm{cos}\:{x}+\mathrm{sin}\:^{\mathrm{2}} {x}+\mathrm{cos}\:^{\mathrm{2}} {x}+\mathrm{sin}\:{x}} \\…

Question-134038

Question Number 134038 by Raxreedoroid last updated on 27/Feb/21 Answered by EDWIN88 last updated on 27/Feb/21 $$\mathrm{V}=\mathrm{2}\pi\underset{\mathrm{0}} {\overset{\mathrm{2}} {\int}}\left(\mathrm{5}−\mathrm{x}\right)\left(\mathrm{8}−\mathrm{x}^{\mathrm{3}} \right)\:\mathrm{dx} \\ $$$$\:\mathrm{V}=\mathrm{2}\pi\underset{\mathrm{0}} {\overset{\mathrm{2}} {\int}}\left(\mathrm{40}−\mathrm{5x}^{\mathrm{3}} −\mathrm{8x}+\mathrm{x}^{\mathrm{4}}…

I-0-1-c-x-2-x-1-x-2-dx-c-gt-1-

Question Number 68481 by ajfour last updated on 11/Sep/19 $${I}=\int_{\mathrm{0}} ^{\:\mathrm{1}} \sqrt{\frac{{c}−{x}^{\mathrm{2}} }{{x}\left(\mathrm{1}−{x}^{\mathrm{2}} \right)}}{dx}\:\:\:\:\:\:\left({c}\:>\mathrm{1}\right) \\ $$ Commented by MJS last updated on 11/Sep/19 $$\mathrm{I}\:\mathrm{tried}\:\mathrm{everything}\:\mathrm{I}\:\mathrm{know},\:\mathrm{it}\:\mathrm{seems}\:\mathrm{impossible} \\…

Given-f-x-x-x-2-1-27-1-3-x-x-2-1-27-1-3-g-x-x-3-x-1-Find-0-4-g-f-g-x-dx-

Question Number 133973 by liberty last updated on 26/Feb/21 $$\:\mathrm{Given}\:\begin{cases}{\mathrm{f}\left(\mathrm{x}\right)=\sqrt[{\mathrm{3}}]{\mathrm{x}+\sqrt{\mathrm{x}^{\mathrm{2}} +\frac{\mathrm{1}}{\mathrm{27}}}}+\sqrt[{\mathrm{3}}]{\mathrm{x}−\sqrt{\mathrm{x}^{\mathrm{2}} +\frac{\mathrm{1}}{\mathrm{27}}}}}\\{\mathrm{g}\left(\mathrm{x}\right)=\mathrm{x}^{\mathrm{3}} +\mathrm{x}+\mathrm{1}}\end{cases} \\ $$$$\mathrm{Find}\:\underset{\mathrm{0}} {\overset{\mathrm{4}} {\int}}\:\left(\mathrm{g}\circ\mathrm{f}\circ\mathrm{g}\right)\left(\mathrm{x}\right)\:\mathrm{dx}\:. \\ $$ Answered by EDWIN88 last updated on…

Question-68434

Question Number 68434 by mhmd last updated on 10/Sep/19 Answered by mind is power last updated on 10/Sep/19 $$\int_{{a}} ^{{b}} {f}\left({x}\right){dx}=\int_{{a}} ^{{b}} {f}\left({a}+\mathrm{b}−\mathrm{x}\right)\mathrm{dx} \\ $$$$\mathrm{let}\:\mathrm{f}\left(\mathrm{x}\right)=\frac{\mathrm{3sin}\left(\mathrm{x}\right)−\mathrm{2sin}^{\mathrm{2}}…

H-2x-1-7-2x-1-9-dx-

Question Number 133972 by liberty last updated on 26/Feb/21 $$\mathscr{H}\:=\:\int\:\frac{\left(\mathrm{2x}−\mathrm{1}\right)^{\mathrm{7}} }{\left(\mathrm{2x}+\mathrm{1}\right)^{\mathrm{9}} }\:\mathrm{dx}\: \\ $$ Answered by EDWIN88 last updated on 26/Feb/21 $$\:\mathscr{H}\:=\:\int\:\left(\frac{\mathrm{2x}−\mathrm{1}}{\mathrm{2x}+\mathrm{1}}\right)^{\mathrm{7}} .\frac{\mathrm{dx}}{\left(\mathrm{2x}+\mathrm{1}\right)^{\mathrm{2}} } \\…