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Category: Integration

does-this-matter-reasonable-sin-x-x-dx-

Question Number 79580 by john santu last updated on 26/Jan/20 $$\mathrm{does}\:\mathrm{this}\:\mathrm{matter}\:\mathrm{reasonable} \\ $$$$\int\:\mathrm{sin}\:^{\mathrm{x}} \left(\mathrm{x}\right)\:\mathrm{dx}\:? \\ $$ Commented by MJS last updated on 26/Jan/20 $$\mathrm{first}\:\mathrm{of}\:\mathrm{all},\:\mathrm{find}\:\mathrm{out}\:\mathrm{where}\:\mathrm{sin}^{{x}} \:{x}\:\mathrm{is}\:\mathrm{defined}……

0-x-x-3-2-x-5-2-4-x-7-2-4-6-1-x-2-2-2-x-4-2-2-4-2-x-6-2-2-4-2-6-2-dx-e-

Question Number 145081 by qaz last updated on 02/Jul/21 $$\int_{\mathrm{0}} ^{\infty} \left(\mathrm{x}−\frac{\mathrm{x}^{\mathrm{3}} }{\mathrm{2}}+\frac{\mathrm{x}^{\mathrm{5}} }{\mathrm{2}\centerdot\mathrm{4}}−\frac{\mathrm{x}^{\mathrm{7}} }{\mathrm{2}\centerdot\mathrm{4}\centerdot\mathrm{6}}+…\right)\centerdot\left(\mathrm{1}+\frac{\mathrm{x}^{\mathrm{2}} }{\mathrm{2}^{\mathrm{2}} }+\frac{\mathrm{x}^{\mathrm{4}} }{\mathrm{2}^{\mathrm{2}} \centerdot\mathrm{4}^{\mathrm{2}} }+\frac{\mathrm{x}^{\mathrm{6}} }{\mathrm{2}^{\mathrm{2}} \centerdot\mathrm{4}^{\mathrm{2}} \centerdot\mathrm{6}^{\mathrm{2}} }+…\right)\mathrm{dx}=\sqrt{\mathrm{e}} \\…

1-0-ln-1-x-x-x-2-1-dx-

Question Number 79531 by jagoll last updated on 26/Jan/20 $$\underset{\mathrm{0}} {\int}^{\mathrm{1}} \:\frac{\mathrm{ln}\left(\frac{\mathrm{1}}{\mathrm{x}}+\mathrm{x}\right)}{\mathrm{x}^{\mathrm{2}} +\mathrm{1}}\mathrm{dx}\:? \\ $$ Commented by john santu last updated on 26/Jan/20 $${remember}\:\underset{\mathrm{0}} {\overset{\infty}…

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}}…