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Category: Integration

Question-158207

Question Number 158207 by tounghoungko last updated on 01/Nov/21 Answered by qaz last updated on 01/Nov/21 $$\mathrm{I}=\int_{\mathrm{0}} ^{\infty} \frac{\mathrm{x}^{\mathrm{5}} \left(\mathrm{e}^{\mathrm{3x}} −\mathrm{e}^{\mathrm{x}} \right)}{\left(\mathrm{e}^{\mathrm{x}} −\mathrm{1}\right)^{\mathrm{4}} }\mathrm{dx} \\…

0-p-x-c-x-dx-

Question Number 92668 by john santu last updated on 08/May/20 $$\underset{\mathrm{0}} {\overset{\mathrm{p}} {\int}}\:\sqrt{\frac{\mathrm{x}}{\mathrm{c}−\mathrm{x}}}\:\mathrm{dx}\:?\: \\ $$ Commented by john santu last updated on 08/May/20 $$\mathrm{set}\:\mathrm{t}\:=\:\sqrt{\frac{{x}}{{c}−{x}}}\:,\:{x}\:=\:\frac{{ct}^{\mathrm{2}} }{\mathrm{1}+{t}^{\mathrm{2}}…

x-2-x-21-2x-3-x-2-8x-4-dx-

Question Number 158176 by Odhiambojr last updated on 31/Oct/21 $$\int\left\{\frac{{x}^{\mathrm{2}} −{x}−\mathrm{21}}{\mathrm{2}{x}^{\mathrm{3}} −{x}^{\mathrm{2}} +\mathrm{8}{x}−\mathrm{4}}\right\}{dx}\: \\ $$ Answered by MJS_new last updated on 31/Oct/21 $$=\int\frac{{x}^{\mathrm{2}} −{x}−\mathrm{21}}{\left(\mathrm{2}{x}−\mathrm{1}\right)\left({x}^{\mathrm{2}} +\mathrm{4}\right)}{dx}=…