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Category: Integration

cos-2xln-1-tan-x-dx-

Question Number 145064 by akolade last updated on 02/Jul/21 $$\:\:\:\:\:\:\int\mathrm{cos}\:\mathrm{2xln}\:\left(\mathrm{1}+\mathrm{tan}\:\mathrm{x}\right)\mathrm{dx} \\ $$$$\:\:\:\:\:\: \\ $$ Answered by mathmax by abdo last updated on 02/Jul/21 $$\Psi=\int\:\mathrm{cos}\left(\mathrm{2x}\right)\mathrm{log}\left(\mathrm{1}+\mathrm{tanx}\right)\mathrm{dx}\:\:\:\mathrm{by}\:\mathrm{parts} \\…

Question-79520

Question Number 79520 by TawaTawa last updated on 25/Jan/20 Commented by mathmax by abdo last updated on 26/Jan/20 $$\Omega\:=\int_{\mathrm{0}} ^{\frac{\mathrm{2}}{\mathrm{5}}} \:\frac{{cos}^{\mathrm{2}} {x}}{{cos}^{\mathrm{2}} \left({x}−\frac{\mathrm{1}}{\mathrm{5}}\right)}{dx}\:=\int_{\mathrm{0}} ^{\frac{\mathrm{2}}{\mathrm{5}}} \:\frac{\mathrm{1}+{cos}\left(\mathrm{2}{x}\right)}{\mathrm{1}+{cos}\left(\mathrm{2}{x}−\frac{\mathrm{2}}{\mathrm{5}}\right)}{dx}…

Question-79516

Question Number 79516 by Pratah last updated on 25/Jan/20 Commented by abdomathmax last updated on 25/Jan/20 $${I}\:=\sum_{{k}=\mathrm{2}} ^{\mathrm{999}} \:\int_{{k}} ^{{k}+\mathrm{1}} {kx}\:{dx}\:=\sum_{{k}=\mathrm{2}} ^{\mathrm{999}} {k}\:\left[\frac{{x}^{\mathrm{2}} }{\mathrm{2}}\right]_{{k}} ^{{k}+\mathrm{1}}…

Question-13977

Question Number 13977 by b.e.h.i.8.3.4.1.7@gmail.com last updated on 25/May/17 Commented by prakash jain last updated on 26/May/17 $$\int\frac{\mathrm{3}+{x}^{\mathrm{2}} }{\mathrm{2}+{x}^{\mathrm{3}} }{dx} \\ $$$$\int\frac{\mathrm{3}}{\left(\mathrm{2}^{\mathrm{1}/\mathrm{3}} \right)^{\mathrm{3}} +{x}^{\mathrm{3}} }{dx}+\int\frac{{x}^{\mathrm{2}}…