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Category: Integration

dx-x-2-8x-15-

Question Number 87023 by john santu last updated on 02/Apr/20 $$\int\:\:\frac{\mathrm{dx}}{\:\sqrt{\mathrm{x}^{\mathrm{2}} −\mathrm{8x}+\mathrm{15}}}\:?\: \\ $$ Commented by john santu last updated on 02/Apr/20 $$\int\:\:\frac{{dx}}{\:\sqrt{\left({x}−\mathrm{4}\right)^{\mathrm{2}} −\mathrm{1}}}\:=\:{I} \\…

0-pi-2-arc-tan-2-tan-x-tan-x-dx-

Question Number 87025 by john santu last updated on 02/Apr/20 $$\underset{\mathrm{0}} {\overset{\frac{\pi}{\mathrm{2}}} {\int}}\:\frac{\mathrm{arc}\:\mathrm{tan}\:\left(\sqrt{\mathrm{2}}\:\mathrm{tan}\:\mathrm{x}\right)}{\mathrm{tan}\:\mathrm{x}}\:\mathrm{dx}?\: \\ $$ Commented by mathmax by abdo last updated on 02/Apr/20 $${let}\:{f}\left({a}\right)\:=\int_{\mathrm{0}}…

6e-x-e-2x-1-dx-

Question Number 86998 by M±th+et£s last updated on 01/Apr/20 $$\int\frac{\mathrm{6}{e}^{{x}} }{{e}^{\mathrm{2}{x}} −\mathrm{1}}\:{dx} \\ $$ Answered by TANMAY PANACEA. last updated on 01/Apr/20 $$\int\frac{\mathrm{6}{d}\left({e}^{{x}} \right)}{\left({e}^{{x}} +\mathrm{1}\right)\left({e}^{{x}}…

Question-152533

Question Number 152533 by mnjuly1970 last updated on 29/Aug/21 Answered by Kamel last updated on 29/Aug/21 $${I}\overset{{t}=\sqrt{{x}}} {=}\mathrm{2}\int_{\mathrm{0}} ^{+\infty} \frac{{Ln}\left(\mathrm{1}+{t}\right)}{{t}\left(\mathrm{1}+{t}\right)}{dt}=\mathrm{2}\int_{\mathrm{0}} ^{\mathrm{1}} \frac{{Ln}\left(\mathrm{1}+{t}\right)}{{t}\left(\mathrm{1}+{t}\right)}{dt}+\mathrm{2}\int_{\mathrm{0}} ^{\mathrm{1}} \frac{{Ln}\left(\mathrm{1}+{t}\right)−{Ln}\left({t}\right)}{\mathrm{1}+{t}}{dt} \\…

Question-86993

Question Number 86993 by Power last updated on 01/Apr/20 Commented by abdomathmax last updated on 01/Apr/20 $${I}\:=\int_{\mathrm{1}} ^{\mathrm{5}} \left[\mathrm{10}{x}\right]{dx}\:\:{vhangement}\:\mathrm{10}{x}\:={t}\:{give} \\ $$$${I}\:=\frac{\mathrm{1}}{\mathrm{10}}\:\int_{\mathrm{10}} ^{\mathrm{50}} \left[{t}\right]{dt}\:=\frac{\mathrm{1}}{\mathrm{10}}\sum_{{k}=\mathrm{10}} ^{\mathrm{49}} \:\int_{{k}}…