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Question Number 60901 Answers: 1 Comments: 0
$${find}\:\int\:\:{arctan}\left(\frac{\mathrm{1}}{\mathrm{1}+{x}^{\mathrm{2}} }\right){dx}\: \\ $$
Question Number 60894 Answers: 0 Comments: 0
$${study}\:{the}\:{convergence}\:{of}\: \\ $$$$\int_{\mathrm{0}} ^{\mathrm{1}} \:\frac{\sqrt{\mathrm{1}+\mathrm{2}{x}}−\sqrt{\mathrm{1}+{x}}}{{ln}\left(\mathrm{1}+{x}\right)}{dx}\:\:{and}\:{determine}\:{its} \\ $$$${value}. \\ $$
Question Number 60893 Answers: 1 Comments: 1
$${calculate}\:\int_{\mathrm{0}} ^{\frac{\pi}{\mathrm{2}}} \:\:\frac{{dx}}{\sqrt{\mathrm{2}}{cos}^{\mathrm{2}} {x}\:+\sqrt{\mathrm{3}}{sin}^{\mathrm{2}} {x}} \\ $$
Question Number 60910 Answers: 1 Comments: 7
Question Number 60888 Answers: 1 Comments: 1
Question Number 60873 Answers: 2 Comments: 5
Question Number 60881 Answers: 0 Comments: 3
$$\underset{−\pi} {\overset{\pi} {\int}}{sin}\left(\frac{\mathrm{1}}{\mathrm{1}−{x}^{\mathrm{2}} }\right)\:{dx} \\ $$
Question Number 60862 Answers: 0 Comments: 0
Question Number 60854 Answers: 2 Comments: 4
$$\left({x}^{\mathrm{4}} −\mathrm{3}{x}^{\mathrm{2}} +\mathrm{2}{x}+\mathrm{1}\right)/\left({x}−\mathrm{1}\right) \\ $$$$ \\ $$$$ \\ $$
Question Number 60853 Answers: 2 Comments: 0
$$\sqrt{\mathrm{5}−\mathrm{12}{i}}+\sqrt{\mathrm{5}+\mathrm{12}{i}}=? \\ $$
Question Number 60849 Answers: 1 Comments: 5
$${For}\:{all}\:\theta\:{in}\:\left[\mathrm{0},\:\pi/\mathrm{2}\right]\:{show}\:{that}\:{cos}\left({sin}\theta\right)\geqslant{sin}\left({cos}\theta\right). \\ $$
Question Number 61612 Answers: 0 Comments: 7
Question Number 60817 Answers: 4 Comments: 2
$$\boldsymbol{\mathrm{V}}=\frac{\mathrm{4}}{\mathrm{3}}\boldsymbol{\pi\mathrm{R}}^{\mathrm{3}} \:\:\:\boldsymbol{\mathrm{prove}} \\ $$
Question Number 60816 Answers: 1 Comments: 0
$$\boldsymbol{\mathrm{S}}=\mathrm{4}\boldsymbol{\pi\mathrm{R}}^{\mathrm{2}} \:\:\:\boldsymbol{\mathrm{prove}} \\ $$
Question Number 60814 Answers: 1 Comments: 0
$${find}\:{x}\:{given}\:{that} \\ $$$$\mathrm{9}^{{sin}^{\mathrm{2}} {x}} +\mathrm{9}^{{cos}^{\mathrm{2}} {x}} =\mathrm{2}\: \\ $$$$ \\ $$
Question Number 60812 Answers: 0 Comments: 5
Question Number 60797 Answers: 0 Comments: 2
$$\int\frac{{e}^{{w}} }{{w}^{{n}+\mathrm{1}} }{dw},\:{n}\in\mathbb{N} \\ $$
Question Number 60791 Answers: 1 Comments: 2
$$\int\frac{{e}^{{n}} }{{x}^{{n}+\mathrm{1}} }{dx},\:\mathrm{n}\in\mathbb{N} \\ $$
Question Number 60788 Answers: 2 Comments: 1
Question Number 60783 Answers: 0 Comments: 2
$$\underset{−\infty} {\overset{\infty} {\int}}{sin}\left(\frac{\mathrm{1}}{\mathrm{1}+{x}^{\mathrm{2}} }\right)\:{dx} \\ $$
Question Number 60775 Answers: 0 Comments: 1
Question Number 60765 Answers: 0 Comments: 2
$${express}\:{in}\:{partial}\:{fraction}\:\mathrm{14}/\left({x}^{\mathrm{2}} +\mathrm{3}\right)\left({x}+\mathrm{2}\right) \\ $$
Question Number 60756 Answers: 1 Comments: 1
$${express}\:{in}\:{partial}\:{fraction}\:\mathrm{5}/\left({x}−\mathrm{2}\right)\left({x}+\mathrm{3}\right)^{\mathrm{2}} \\ $$
Question Number 60748 Answers: 1 Comments: 1
Question Number 60745 Answers: 4 Comments: 5
Question Number 60739 Answers: 1 Comments: 4
$${evaluate}\:\: \\ $$$${i}.\int\:\left(\frac{{x}+\mathrm{1}}{{x}−\mathrm{1}}\right){dx} \\ $$$${ii}.\:\:\int_{\mathrm{0}} ^{\pi} \left(\mathrm{2}{cosxsinx}\right){dx}\:\: \\ $$$${iii}.\:\:\int_{\frac{\pi}{\mathrm{3}\:}\:} ^{\pi} \left(\frac{{sin}\mathrm{2}{x}}{{cos}\mathrm{2}{x}}\right){dx} \\ $$
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