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IntegrationQuestion and Answers: Page 151

Question Number 101835    Answers: 3   Comments: 0

$$\underset{\mathrm{0}} {\overset{\infty} {\int}}\frac{\mathrm{1}}{{e}^{{x}} +\mathrm{1}}\:{dx}\: \\ $$

Question Number 101833    Answers: 3   Comments: 0

$$\int\:_{−\mathrm{1}} ^{\mathrm{1}} \sqrt{\frac{\mathrm{1}+{x}}{\mathrm{1}−{x}}}\:{dx}\:?\: \\ $$

Question Number 101816    Answers: 1   Comments: 0

$$\int_{\mathrm{1}} ^{\:\:{e}} \left(\frac{{tan}^{−\mathrm{1}} {x}}{{x}}+\frac{{log}}{{x}^{\mathrm{2}} +\mathrm{1}}\right){dx} \\ $$

Question Number 101808    Answers: 2   Comments: 0

$$\int_{\frac{\mathrm{1}}{\mathrm{3}}} ^{\mathrm{1}} \frac{\left(\mathrm{x}−\mathrm{x}^{\mathrm{3}} \right)^{\mathrm{1}/\mathrm{3}} }{\mathrm{x}^{\mathrm{4}} }\mathrm{dx} \\ $$

Question Number 101793    Answers: 1   Comments: 0

$$\int_{\mathrm{1}} ^{\mathrm{2}} \frac{{logu}}{\left(\sqrt{{u}−\mathrm{1}}\right)\left(\sqrt{{u}−\mathrm{1}}+\mathrm{1}\right)}{du} \\ $$

Question Number 101791    Answers: 2   Comments: 0

$$\frac{\mathrm{1}}{{n}^{\mathrm{3}\:\:} }\underset{{n}\rightarrow\infty} {\mathrm{lim}}\left({ne}^{−\left(\frac{\mathrm{1}}{{n}}\right)^{\mathrm{2}} } +\mathrm{2}{ne}^{−\left(\frac{\mathrm{2}}{{n}}\right)^{\mathrm{2}} } +....\infty\right) \\ $$

Question Number 101783    Answers: 2   Comments: 0

$$\int_{\:\mathrm{0}} ^{\:\mathrm{1}} \:\:\frac{\mathrm{ln}\left(\mathrm{x}^{\mathrm{2}} \:+\:\mathrm{1}\right)}{\mathrm{x}\:\:+\:\:\mathrm{1}} \\ $$

Question Number 101775    Answers: 0   Comments: 1

$$\int{x}^{{x}^{{x}} } \centerdot{x}^{{x}} \centerdot{xdx}=? \\ $$$${or}\:{it}\:{able}\:{to}\:{solve}? \\ $$

Question Number 101747    Answers: 1   Comments: 0

$$\int\frac{{x}^{\frac{−\mathrm{1}}{\mathrm{2}}} }{\mathrm{1}+{x}^{\frac{\mathrm{1}}{\mathrm{3}}} }{dx} \\ $$

Question Number 101650    Answers: 2   Comments: 1

Question Number 101633    Answers: 1   Comments: 2

$$\int\mathrm{x}^{\mathrm{x}^{\mathrm{x}} } \centerdot\mathrm{x}^{\mathrm{x}} \centerdot\mathrm{x}\:\mathrm{dx}=? \\ $$

Question Number 101608    Answers: 0   Comments: 0

$$\int_{\mathrm{0}\:} ^{\frac{\pi}{\mathrm{2}}} {ln}\left(\frac{{ln}^{\mathrm{2}} \left({sin}\left(\theta\right)\right)}{\pi^{\mathrm{2}} +{ln}^{\mathrm{2}} \left({sin}\left(\theta\right)\right)}\right)\frac{{ln}\left({cos}\left(\theta\right)\right)}{{tan}\left(\theta\right)}{d}\theta \\ $$

Question Number 101601    Answers: 1   Comments: 0

$$\int_{\sqrt{\mathrm{2}}−\mathrm{1}} ^{\sqrt{\mathrm{2}}+\mathrm{1}} \frac{{x}^{\mathrm{4}} +{x}^{\mathrm{2}} +\mathrm{1}}{\left({x}^{\mathrm{2}} +\mathrm{1}\right)^{\mathrm{2}} }{dx} \\ $$

Question Number 101597    Answers: 0   Comments: 3

$$\:\int\:\mathrm{ln}\:\left(\mathrm{1}+\:{e}^{{x}} \right)\:{dx}\:=\:.. \\ $$

Question Number 101585    Answers: 1   Comments: 0

$$\int_{\mathrm{0}} ^{\pi} \frac{\mathrm{1}}{{a}^{\mathrm{2}} −\mathrm{2}{a}\:{cosx}\:+\:\mathrm{1}}{dx}\:\left({a}<\mathrm{1}\right)\:{is} \\ $$$$ \\ $$

Question Number 101860    Answers: 1   Comments: 1

Question Number 101531    Answers: 1   Comments: 0

$${find}\:\int\sqrt{{ax}−{x}^{\mathrm{2}} }{dx} \\ $$

Question Number 101493    Answers: 1   Comments: 0

$$\int\sqrt{\mathrm{x}.\sqrt[{\mathrm{3}}]{\mathrm{x}.\sqrt[{\mathrm{4}}]{\mathrm{x}.\sqrt[{\mathrm{5}}]{\mathrm{x}.\sqrt[{\mathrm{6}}]{\mathrm{x}.\sqrt[{\mathrm{7}}]{\mathrm{x}...}}}}}}\:\mathrm{dx}\:=\: \\ $$$$ \\ $$

Question Number 101486    Answers: 0   Comments: 0

Question Number 101461    Answers: 1   Comments: 0

Question Number 101451    Answers: 2   Comments: 1

Question Number 105239    Answers: 1   Comments: 0

$$\underset{\underset{{p}=\mathrm{5}} {\overset{\mathrm{6}} {\sum}}{p}} {\overset{\underset{{p}=\mathrm{8}} {\overset{\mathrm{11}} {\sum}}{p}} {\sum}}\:\underset{\mathrm{11}} {\overset{\mathrm{13}} {\int}}\left(\frac{\mathrm{12}{ky}}{{x}^{\mathrm{2}} }\:+\:\mathrm{6}{x}\right)\:{dx}\:=\:\underset{\underset{{p}=\mathrm{4}} {\overset{\mathrm{7}} {\sum}}{p}} {\overset{\underset{{p}=\mathrm{9}} {\overset{\mathrm{12}} {\sum}}{p}} {\sum}}\:\underset{\mathrm{11}} {\overset{\mathrm{16}} {\int}}\left({x}^{\mathrm{2}} {y}−\frac{\mathrm{3}}{\mathrm{2}}{k}\right){dx} \\ $$$${solve}\:{for}\:{y} \\ $$

Question Number 101378    Answers: 2   Comments: 1

$$\int_{\frac{\mathrm{1}}{{e}}} ^{{tanx}} \frac{{t}}{\mathrm{1}+{t}^{\mathrm{2}} }{dt}\:+\:\int_{\frac{\mathrm{1}}{{e}}} ^{{cotx}} \frac{\mathrm{1}}{{t}\left(\mathrm{1}+{t}^{\mathrm{2}} \right)}{dt} \\ $$

Question Number 101373    Answers: 0   Comments: 1

$$\underset{{n}\rightarrow\infty\:} {\mathrm{lim}}\underset{{r}=\mathrm{1}} {\overset{\mathrm{4}{n}} {\sum}}\frac{\sqrt{{n}}}{\sqrt{{r}}\left(\mathrm{3}\sqrt{{r}}+\mathrm{4}\sqrt{{n}}\right)^{\mathrm{2}} } \\ $$

Question Number 101345    Answers: 0   Comments: 3

$$\left(\mathrm{1}\right)\int\:\frac{\mathrm{sec}\:^{\mathrm{4}} {x}\:\mathrm{tan}\:{x}}{\mathrm{sec}\:^{\mathrm{4}} {x}+\mathrm{4}}\:{dx}= \\ $$$$\left(\mathrm{2}\right)\:\int{x}^{\mathrm{2}{x}} \left(\mathrm{2ln}{x}\:+\mathrm{2}\right)\:{dx}\:= \\ $$$$\left(\mathrm{3}\right)\:\underset{\mathrm{0}} {\overset{\mathrm{1}} {\int}}\:\sqrt{\mathrm{1}−{x}^{\mathrm{2}} }\:{dx}\:=\: \\ $$

Question Number 101328    Answers: 0   Comments: 1

$${this}\:{i}\:{a}\:{beautifull}\:{old}\:{question}\:{in}\:{the}\:{forum} \\ $$$${by}\:{sir}.{Ali}\:{Esam}\:{i}\:{Reposted}\:{it}\:{trying}\:{to} \\ $$$${find}\:{any}\:{idea}\:{to}\:{solve} \\ $$$$ \\ $$$${I}=\int_{−\mathrm{1}} ^{\mathrm{1}} \left(\frac{{sin}\left({x}\right)}{{sinh}^{−\mathrm{1}} \left({x}\right)}\right)\left(\frac{{sin}^{−\mathrm{1}} \left({x}\right)}{{sinh}\left({x}\right)}\right){dx} \\ $$$$ \\ $$$${i}\:{solved}\:{it}\:{numerical}\: \\ $$$${the}\:{value}\:{is}\:\mathrm{2}.\mathrm{03383} \\ $$

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