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IntegrationQuestion and Answers: Page 125
Question Number 117817 Answers: 2 Comments: 1
Question Number 117811 Answers: 1 Comments: 0
$$\int_{\:\mathrm{0}} ^{\:\boldsymbol{\pi}} \boldsymbol{\mathrm{ln}}\mid\boldsymbol{\mathrm{sinh}}\left(\boldsymbol{\mathrm{x}}\right)\mid\boldsymbol{\mathrm{dx}} \\ $$
Question Number 117806 Answers: 4 Comments: 2
$$\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:...\:{nice}\:\:{calculus}... \\ $$$$\:\:\:\:{i}\:::\:\:\:\mathrm{1}\:+\frac{\mathrm{4}}{\mathrm{9}}+\frac{\mathrm{9}}{\mathrm{36}}+\frac{\mathrm{16}}{\mathrm{100}}+...=\:?? \\ $$$$\:\:\:\:\:{ii}::\:\:\int_{\mathrm{0}} ^{\:\frac{\pi}{\mathrm{2}}} {x}^{\mathrm{2}} {cot}\left({x}\right)\:{dx}=?? \\ $$$$\:\:\:\:\:\:\:\:\:\:\:\:\:\:{m}.{n}.\mathrm{1970} \\ $$$$ \\ $$
Question Number 117724 Answers: 2 Comments: 5
$$\int\:\frac{\mathrm{sin}^{β\mathrm{1}} \left(\mathrm{x}\right)}{\mathrm{x}^{\mathrm{2}} }\:\mathrm{dx}\:=? \\ $$
Question Number 117655 Answers: 0 Comments: 3
Question Number 117654 Answers: 0 Comments: 1
Question Number 117638 Answers: 2 Comments: 0
$$\underset{\mathrm{0}} {\overset{\mathrm{1}} {\int}}\:\frac{\mathrm{2x}^{\mathrm{12}} +\mathrm{5x}^{\mathrm{9}} }{\left(\mathrm{x}^{\mathrm{5}} +\mathrm{x}^{\mathrm{3}} +\mathrm{1}\right)^{\mathrm{3}} }\:\mathrm{dx}\:=?\: \\ $$
Question Number 117574 Answers: 1 Comments: 0
$$\:\:\:\:\:\:\:\:...\:{advanced}\:\:{integral}... \\ $$$$\:\:\:\:\:\: \\ $$$$\mathscr{E}{valuate}\:::\: \\ $$$$\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\mathrm{I}\::=\:\int_{\mathrm{0}} ^{\:\infty} \frac{\:\mathrm{4}{xln}\left({x}\right)}{{x}^{\mathrm{4}} +\mathrm{2}{x}^{\mathrm{2}} +\mathrm{4}\:}{dx}\:=??\: \\ $$$$\:\:\:\:\:...\:{m}.{n}.\mathrm{1970}.. \\ $$$$\: \\ $$
Question Number 117527 Answers: 1 Comments: 0
$$\int_{\:\mathrm{0}} ^{\:\mathrm{1}} \mathrm{xsec}\left(\mathrm{2x}\right)\mathrm{dx} \\ $$
Question Number 117511 Answers: 3 Comments: 0
Question Number 117496 Answers: 2 Comments: 0
$$\int\:\frac{\mathrm{sec}\:^{\mathrm{2}} \theta\:\mathrm{tan}\:^{\mathrm{2}} \theta}{\:\sqrt{\mathrm{9}β\mathrm{tan}\:^{\mathrm{2}} \theta}}\:\mathrm{d}\theta\:=? \\ $$
Question Number 117463 Answers: 0 Comments: 2
Question Number 117446 Answers: 2 Comments: 0
$$\mathrm{Evaluate}\:\int\frac{\mathrm{3}{x}^{\mathrm{2}} β\mathrm{5}}{{x}^{\mathrm{4}} +\mathrm{6}{x}^{\mathrm{2}} +\mathrm{25}}\mathrm{d}{x} \\ $$
Question Number 117437 Answers: 2 Comments: 0
$$\int_{\mathrm{0}} ^{\infty} \frac{{dx}}{{a}^{\mathrm{3}} +{x}^{\mathrm{3}} } \\ $$$$ \\ $$$${generaly} \\ $$$$\int_{\mathrm{0}} ^{\infty} \frac{{dx}}{{p}+{x}^{{n}} } \\ $$
Question Number 117431 Answers: 0 Comments: 0
Question Number 117409 Answers: 1 Comments: 0
Question Number 117403 Answers: 1 Comments: 1
$$\:\:\:\underset{\mathrm{0}} {\overset{\mathrm{1}} {\int}}\:\left(\mathrm{arc}\:\mathrm{tan}\:\mathrm{x}\right)^{\mathrm{2}} \:\mathrm{dx}\:=? \\ $$
Question Number 117396 Answers: 3 Comments: 0
$$\:\:\:\:\:\:\:\:...{differential}\:\:{equation}...\: \\ $$$$ \\ $$$$\:\:\:\:{solve}\:: \\ $$$$ \\ $$$$\:\:\:\:\:\:\:\:\:\:\:\:\frac{{dy}}{{dx}}=\frac{\mathrm{1}}{{xy}+\mathrm{2}{x}^{\mathrm{2}} {y}} \\ $$$$\:\:\:\:\:\:\:\:\:{general}\:\:{solution}\:=??? \\ $$$$\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:{m}.{n}.\mathrm{1970} \\ $$$$\: \\ $$
Question Number 117380 Answers: 1 Comments: 1
$$\:\:\:\:\:\:\:\:\:\:\:...\:\:{prove}\:\:{that}\:... \\ $$$$\:\: \\ $$$$\Omega=\int_{\mathrm{0}} ^{\:\infty} \frac{\mathrm{1}}{\mathrm{2}\sqrt{{x}}}{sin}\left(\pi^{\mathrm{2}} {x}+\frac{\mathrm{1}}{{x}}\right){dx}=\frac{\mathrm{1}}{\:\sqrt{\mathrm{8}\pi}} \\ $$$$ \\ $$$$\:\:\:\:\:\:{m}.{n}.\mathrm{1970} \\ $$
Question Number 117348 Answers: 0 Comments: 1
Question Number 117342 Answers: 2 Comments: 0
$$\:\left(\mathrm{1}\right)\int\:\left(\mathrm{tan}^{β\mathrm{1}} \left(\mathrm{x}\right)\right)^{\mathrm{2}} \:\mathrm{dx}\:=\:? \\ $$$$\left(\mathrm{2}\right)\:\int\:\mathrm{tan}^{β\mathrm{1}} \left(\sqrt{\mathrm{x}}\right)\:\mathrm{dx}\:=? \\ $$
Question Number 117329 Answers: 1 Comments: 0
$$\:\:\:\:\:\:\:\:\:{nice}\:\:{math} \\ $$$$\:\:{evaluate}:: \\ $$$$ \\ $$$$\:\:\:\: \\ $$$$\:\: \\ $$$$ \\ $$$$\:\:\:\Omega=\int_{\mathrm{0}} ^{\:\mathrm{1}} \frac{{arctan}\left({x}\right).{ln}\left(\mathrm{1}β{x}\right)}{\mathrm{1}+{x}^{\mathrm{2}} }{dx}??? \\ $$$$\:\:\:\:\:\:\:\:\:{m}.{n}.\mathrm{1970} \\ $$$$ \\ $$
Question Number 117311 Answers: 2 Comments: 0
Question Number 117253 Answers: 3 Comments: 0
$$\mathrm{calculate}\:\int_{β\infty} ^{\infty} \:\:\frac{\mathrm{x}^{\mathrm{2}} }{\left(\mathrm{x}^{\mathrm{2}} β\mathrm{x}\:+\mathrm{1}\right)^{\mathrm{2}} }\mathrm{dx} \\ $$
Question Number 117249 Answers: 1 Comments: 0
$$\mathrm{calculate}\:\int_{\mathrm{0}} ^{\infty} \:\:\frac{\left(β\mathrm{1}\right)^{\mathrm{x}^{\mathrm{2}} } }{\mathrm{x}^{\mathrm{4}} \:+\mathrm{x}^{\mathrm{2}} \:+\mathrm{1}}\mathrm{dx}\: \\ $$
Question Number 117227 Answers: 0 Comments: 0
$${why}\:{every}\:{function}\:{that}\:{is}\:{Riemann} \\ $$$${integrable}\:{is}\:{not}\:{lebsgue}\:{integrable}? \\ $$
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