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Category: Integration

dx-x-4-4-

Question Number 209543 by Spillover last updated on 13/Jul/24 $$\:\: \\ $$$$\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\int\frac{{dx}}{{x}^{\mathrm{4}} +\mathrm{4}} \\ $$$$ \\ $$ Commented by Frix last updated on 14/Jul/24 $$\mathrm{Done}\:\mathrm{several}\:\mathrm{times}\:\mathrm{before}…

Question-209353

Question Number 209353 by alcohol last updated on 08/Jul/24 Answered by Berbere last updated on 08/Jul/24 $${f}\left({x}+{y}\right)={f}\left({x}\right).{f}\left({y}\right) \\ $$$${f}\left({x}\right)={f}\left(\frac{{x}}{\mathrm{2}}+\frac{{x}}{\mathrm{2}}\right)=\left({f}\left(\frac{{x}}{\mathrm{2}}\right)\right)^{\mathrm{2}} \geqslant\mathrm{0} \\ $$$$\forall{x}\in\mathbb{R}\:{f}\left({x}\right)\geqslant\mathrm{0} \\ $$$${f}\left({x}+{y}\right)={f}\left({x}\right){f}\left({y}\right)\:\forall{y}\in\mathbb{R}\:{fixe}\:{x}\rightarrow{f}\left({x}+{y}\right)\:{est}\:{derivable} \\…

Question-209332

Question Number 209332 by efronzo1 last updated on 07/Jul/24 Answered by Frix last updated on 07/Jul/24 $${x}^{\mathrm{3}} −\mathrm{8}{x}^{\mathrm{2}} +\left(\mathrm{16}−{k}\right){x}=\mathrm{0} \\ $$$${x}_{\mathrm{1}} =\mathrm{0}\:\:{x}_{\mathrm{2}} =\mathrm{4}−\sqrt{{k}}\:\:{x}_{\mathrm{3}} =\mathrm{4}+\sqrt{{k}} \\…

calculate-I-0-tan-1-x-1-x-2-2-dx-

Question Number 209217 by mnjuly1970 last updated on 04/Jul/24 $$ \\ $$$$\:\:\:\:\:\:\:\:\:\:\:\:\boldsymbol{{calculate}}\:: \\ $$$$\:\:\:\: \\ $$$$\:\:\:\:\:\:\:\:\:\:\:\mathrm{I}=\:\int_{\mathrm{0}\:} ^{\:\infty} \frac{\:{tan}^{\:−\mathrm{1}} \left({x}\right)}{\left(\mathrm{1}\:+\:{x}^{\:\mathrm{2}} \right)^{\:\mathrm{2}} }\:{dx}\:=\:?\:\:\:\:\: \\ $$$$ \\ $$…

L-0-1-4-3x-4-5x-dx-

Question Number 208871 by Shrodinger last updated on 26/Jun/24 $${L}=\int_{\mathrm{0}} ^{\mathrm{1}} \sqrt{\frac{\mathrm{4}−\mathrm{3}{x}}{\mathrm{4}+\mathrm{5}{x}}}{dx} \\ $$ Answered by Sutrisno last updated on 26/Jun/24 $${misal} \\ $$$$\sqrt{\frac{\mathrm{4}−\mathrm{3}{x}}{\mathrm{4}+\mathrm{5}{x}}}={p}\rightarrow{x}=\frac{−\mathrm{4}{p}^{\mathrm{2}} +\mathrm{4}}{\mathrm{5}{p}^{\mathrm{2}}…