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Category: Integration

calculate-1-dx-x-2-1-x-2-3-

Question Number 98179 by abdomathmax last updated on 12/Jun/20 $$\mathrm{calculate}\:\int_{\mathrm{1}} ^{+\infty} \:\:\:\frac{\mathrm{dx}}{\mathrm{x}^{\mathrm{2}} \left(\mathrm{1}−\mathrm{x}^{\mathrm{2}} \right)^{\mathrm{3}} } \\ $$ Answered by MJS last updated on 12/Jun/20 $$\mathrm{I}\:\mathrm{love}\:\mathrm{Ostrogradski}'\mathrm{s}\:\mathrm{Method}……

CALCULUS-0-1-x-2n-1-x-1-dx-n-1-

Question Number 163709 by amin96 last updated on 09/Jan/22 $$\boldsymbol{\mathrm{CALCULUS}} \\ $$$$\int_{\mathrm{0}} ^{\mathrm{1}} \frac{\boldsymbol{\mathrm{x}}^{\mathrm{2}\boldsymbol{\mathrm{n}}−\mathrm{1}} }{\boldsymbol{\mathrm{x}}+\mathrm{1}}\boldsymbol{\mathrm{dx}}=?\:\:\:\:\:\boldsymbol{\mathrm{n}}\geqslant\mathrm{1} \\ $$ Answered by Mathspace last updated on 09/Jan/22 $$\int_{\mathrm{0}}…

plzz-help-ne-differentiate-between-sin-2x-1-2-cox-2x-c-is-not-change-to-2sin-x-cos-x-but-b-a-sin-2x-is-change-to-b-a-2sin-x-cos-x-

Question Number 32627 by Cheyboy last updated on 29/Mar/18 $${plzz}\:{help}\:{ne}\:{differentiate}\: \\ $$$${between} \\ $$$$\int{sin}\left(\mathrm{2}{x}\right)=\:−\frac{\mathrm{1}}{\mathrm{2}}{cox}\left(\mathrm{2}{x}\right)+{c}\: \\ $$$${is}\:{not}\:{change}\:{to}\:\int\mathrm{2}{sin}\left({x}\right){cos}\left({x}\right) \\ $$$${but}\:\underset{{b}} {\overset{{a}} {\int}}{sin}\left(\mathrm{2}{x}\right)=\:{is}\:{change}\:{to} \\ $$$$\underset{{b}} {\overset{{a}} {\int}}\mathrm{2}{sin}\left({x}\right){cos}\left({x}\right) \\…

e-x-5-8x-2-dx-pi-4-2-e-x-5-erfi-2-2-x-5-pi-4-128-2-super-erf-hyper-2-2-x-c-where-super-erf-hyper-t-is-super-function-in-D-2-and-D-n-

Question Number 98151 by  M±th+et+s last updated on 11/Jun/20 $$\int{e}^{{x}^{\mathrm{5}} +\mathrm{8}{x}^{\mathrm{2}} } {dx} \\ $$$$=\frac{\sqrt{\pi}}{\mathrm{4}\sqrt{\mathrm{2}}}{e}^{{x}^{\mathrm{5}} } {erfi}\left(\mathrm{2}\sqrt{\mathrm{2}}{x}\right)−\frac{\mathrm{5}\sqrt{\pi}}{\mathrm{4}\left(\mathrm{128}\right)\sqrt{\mathrm{2}}}\left({super}−{erf}_{\left({hyper}\right)} \left(\mathrm{2}\sqrt{\mathrm{2}}{x}\right)\right)+{c} \\ $$$$ \\ $$$${where}\left[{super}−{erf}_{\left({hyper}\right)} \left({t}\right)\right]\:{is}\:{super}−{function} \\ $$$${in}\:{D}_{\mathrm{2}}…