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Category: Integration

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

Question Number 98016 by bemath last updated on 11/Jun/20 $$\underset{\mathrm{0}} {\overset{\mathrm{1}} {\int}}\:\frac{\mathrm{ln}^{\mathrm{2}} \left({x}\right)}{{x}^{\mathrm{2}} +\mathrm{1}}\:{dx}\:?\: \\ $$ Commented by bobhans last updated on 11/Jun/20 $$\mathrm{substitution}\:{w}\:=\:−\mathrm{ln}\:\left({x}\right)\:,\:{x}\:=\:{e}^{−{w}} \\…

0-x-3-e-x-1-dx-

Question Number 163490 by Zaynal last updated on 07/Jan/22 $$\int_{\mathrm{0}} ^{\infty} \:\frac{\boldsymbol{{x}}^{\mathrm{3}} }{\boldsymbol{{e}}^{\boldsymbol{{x}}} \:−\mathrm{1}}\:\boldsymbol{{dx}} \\ $$ Answered by mnjuly1970 last updated on 07/Jan/22 $$\:\:\:\:\Gamma\:\left(\mathrm{4}\right).\zeta\:\left(\mathrm{4}\right)=\:\frac{\pi^{\:\mathrm{4}} }{\mathrm{15}}…

Question-163483

Question Number 163483 by Zaynal last updated on 07/Jan/22 Answered by alephzero last updated on 07/Jan/22 $$\int_{\mathrm{0}} ^{\mathrm{1}} \mathrm{4}{x}^{\mathrm{3}} \left\{\frac{{d}^{\mathrm{2}} }{{dx}^{\mathrm{2}} }\left(\mathrm{1}−{x}^{\mathrm{2}} \right)^{\mathrm{5}} \right\}{dx}\:=\:? \\…