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Category: Integration

For-witch-value-of-the-integral-I-0-1-1-2x-2-1-x-dx-converge-and-in-this-case-calculate-

Question Number 79869 by Henri Boucatchou last updated on 28/Jan/20 $${For}\:\:{witch}\:\:{value}\:\:{of}\:\:\alpha\:\:{the}\:\:{integral} \\ $$$$\:\:{I}=\int_{\mathrm{0}} ^{\infty} \left(\frac{\mathrm{1}}{\:\sqrt{\mathrm{1}+\mathrm{2}{x}^{\mathrm{2}} }}−\frac{\alpha}{\mathrm{1}+{x}}\right){dx}\:\:{converge}; \\ $$$$\:\:{and}\:\:{in}\:\:{this}\:\:{case}\:\:{calculate}\:\:\alpha \\ $$ Commented by mathmax by abdo…

0-pi-2-1-cos-2x-sin-2x-ln-sec-x-1-3-dx-

Question Number 145385 by mnjuly1970 last updated on 04/Jul/21 $$\int_{\mathrm{0}} ^{\:\frac{\pi}{\mathrm{2}}} \frac{\mathrm{1}+\mathrm{cos}\:\left(\mathrm{2x}\right)}{\mathrm{sin}\:\left(\mathrm{2x}\:\right)}.\:\mathrm{ln}\sqrt[{\mathrm{3}}]{\mathrm{sec}\:\left(\mathrm{x}\right)}\:\mathrm{dx}=? \\ $$ Answered by mindispower last updated on 04/Jul/21 $${cos}\left(\mathrm{2}{x}\right)=\mathrm{2}{cos}^{\mathrm{2}} \left({x}\right)−\mathrm{1} \\ $$$$\Leftrightarrow−\frac{\mathrm{1}}{\mathrm{3}}\int_{\mathrm{0}}…

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

Question Number 79825 by TawaTawa last updated on 28/Jan/20 $$\int_{\:\mathrm{0}} ^{\:\mathrm{1}} \:\sqrt{\mathrm{x}^{\mathrm{3}} \:+\:\mathrm{1}}\:\:\mathrm{dx} \\ $$ Commented by MJS last updated on 28/Jan/20 $$\mathrm{only}\:\mathrm{possible}\:\mathrm{to}\:\mathrm{approximate} \\ $$$$\approx\mathrm{1}.\mathrm{11144797}…

3-dx-x-3-2-

Question Number 14287 by tawa tawa last updated on 30/May/17 $$\int_{\:\:\mathrm{3}} ^{\:\:\infty} \:\:\frac{\mathrm{dx}}{\left(\mathrm{x}\:−\:\mathrm{3}\right)^{\mathrm{2}} } \\ $$ Commented by prakash jain last updated on 30/May/17 $$\mathrm{No}\:\mathrm{answer}\:\mathrm{integral}\:\mathrm{does}\:\mathrm{not}…

Evaluate-0-1-ln-1-x-2-arctan-x-dx-

Question Number 145358 by qaz last updated on 04/Jul/21 $$\mathrm{Evaluate}::\:\:\:\int_{\mathrm{0}} ^{\mathrm{1}} \mathrm{ln}\left(\mathrm{1}+\mathrm{x}^{\mathrm{2}} \right)\centerdot\mathrm{arctan}\left(\mathrm{x}\right)\mathrm{dx}=? \\ $$ Answered by Olaf_Thorendsen last updated on 04/Jul/21 $$\mathrm{I}\:=\:\int_{\mathrm{0}} ^{\mathrm{1}} \mathrm{ln}\left(\mathrm{1}+{x}^{\mathrm{2}}…