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Category: Integration

Question-130326

Question Number 130326 by rs4089 last updated on 24/Jan/21 Answered by Lordose last updated on 24/Jan/21 $$ \\ $$$$\Omega\left(\mathrm{p}\right)\:=\:\int_{\mathrm{0}} ^{\:\infty} \frac{\mathrm{sin}\left(\mathrm{px}\right)}{\mathrm{x}\left(\mathrm{x}^{\mathrm{2}} +\mathrm{1}\right)}\mathrm{dx} \\ $$$$\Omega'\left(\mathrm{p}\right)\:=\:\int_{\mathrm{0}} ^{\:\infty}…

x-1-x-2-x-2-2x-2-2-dx-

Question Number 130320 by benjo_mathlover last updated on 24/Jan/21 $$\:\int\:\frac{\mathrm{x}−\mathrm{1}}{\left(\mathrm{x}−\mathrm{2}\right)\left(\mathrm{x}^{\mathrm{2}} −\mathrm{2x}+\mathrm{2}\right)^{\mathrm{2}} }\:\mathrm{dx}\: \\ $$ Answered by EDWIN88 last updated on 24/Jan/21 $$\mathrm{Let}\:\mathcal{E}\:=\:\int\:\frac{{x}−\mathrm{1}}{\left({x}−\mathrm{2}\right)\left({x}^{\mathrm{2}} −\mathrm{2}{x}+\mathrm{2}\right)^{\mathrm{2}} }\:{dx} \\…

0-x-cos-x-ln-x-e-x-dx-

Question Number 130306 by benjo_mathlover last updated on 24/Jan/21 $$\int_{\mathrm{0}} ^{\:\infty} \:\mathrm{x}\:\mathrm{cos}\:\left(\mathrm{x}\right)\:\mathrm{ln}\:\left(\mathrm{x}\right)\mathrm{e}^{−\mathrm{x}} \:\mathrm{dx}\:?\: \\ $$ Answered by Dwaipayan Shikari last updated on 24/Jan/21 $${I}\left({a}\right)=\int_{\mathrm{0}} ^{\infty}…

Given-that-g-x-2-1-x-1-3x-2-a-express-g-x-in-partial-fractions-b-evaluate-0-1-g-x-dx-

Question Number 64762 by Lontum Hans-Sandys last updated on 21/Jul/19 $$\mathrm{Given}\:\mathrm{that}\:\mathrm{g}\left(\mathrm{x}\right)=\frac{\mathrm{2}}{\left(\mathrm{1}+\mathrm{x}\right)\left(\mathrm{1}+\mathrm{3x}^{\mathrm{2}} \right.} \\ $$$$\left.\mathrm{a}\right)\:\mathrm{express}\:\mathrm{g}\left(\mathrm{x}\right)\:\mathrm{in}\:\mathrm{partial}\:\mathrm{fractions}. \\ $$$$\left.\mathrm{b}\right)\:\mathrm{evaluate}\:\int_{\mathrm{0}} ^{\mathrm{1}} \mathrm{g}\left(\left(\mathrm{x}\right)\:\mathrm{dx}.\right. \\ $$ Commented by mathmax by abdo…

x-2-2-x-dx-

Question Number 130296 by sumit Singh last updated on 24/Jan/21 $$\int\left({x}^{\mathrm{2}} /\mathrm{2}+{x}\right){dx} \\ $$ Commented by EDWIN88 last updated on 24/Jan/21 $$\int\:\left(\frac{\mathrm{x}^{\mathrm{2}} }{\mathrm{2}}+\mathrm{x}\right)\mathrm{dx}\:\mathrm{or}\:\int\:\frac{\mathrm{x}^{\mathrm{2}} }{\mathrm{2}+\mathrm{x}}\:\mathrm{dx}\:? \\…

Question-130285

Question Number 130285 by Lordose last updated on 23/Jan/21 Answered by Olaf last updated on 24/Jan/21 $$\Omega\:=\:\int_{\mathrm{2}} ^{\mathrm{6}} \underset{{k}=\mathrm{1}} {\overset{\mathrm{9}} {\prod}}\left({x}−{k}\right){dx} \\ $$$$\mathrm{Let}\:{u}\:=\:{x}−\mathrm{5} \\ $$$$\Omega\:=\:\int_{−\mathrm{3}}…