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Question Number 85620 Answers: 1 Comments: 0
$${prove}\:{that} \\ $$$$ \\ $$$$\mathrm{cosh}\:\left({x}−{y}\right)=\mathrm{cosh}\:{x}\mathrm{cosh}\:{y}−\mathrm{sinh}\:{x}\mathrm{sinh}\:{y} \\ $$
Question Number 85606 Answers: 0 Comments: 7
Question Number 85603 Answers: 0 Comments: 0
$${prove}\:{the}\:{relation} \\ $$$$\int_{\mathrm{0}} ^{\mathrm{1}} \frac{{li}_{\mathrm{5}} \left(\sqrt[{\mathrm{5}}]{{x}}\right)}{\sqrt[{\mathrm{5}}]{{x}}}{dx}=\frac{\mathrm{5}}{\mathrm{4}}\left(\frac{\mathrm{25}}{\mathrm{3072}}−\frac{\zeta\left(\mathrm{2}\right)}{\mathrm{2}^{\mathrm{6}} }+\frac{\zeta\left(\mathrm{3}\right)}{\mathrm{2}^{\mathrm{4}} }−\frac{\zeta\left(\mathrm{4}\right)}{\mathrm{2}^{\mathrm{2}} }+\zeta\left(\mathrm{5}\right)\right) \\ $$
Question Number 85592 Answers: 1 Comments: 0
$$\int\frac{\left(\mathrm{u}+\mathrm{1}\right)^{\mathrm{2}} }{\mathrm{u}^{\mathrm{3}} +\mathrm{u}}\mathrm{du} \\ $$
Question Number 85591 Answers: 1 Comments: 0
$$\int\frac{\mathrm{1}+\mathrm{4u}}{−\mathrm{4u}^{\mathrm{2}} +\mathrm{2u}+\mathrm{2}}\mathrm{du} \\ $$$$ \\ $$
Question Number 85590 Answers: 0 Comments: 0
Question Number 85588 Answers: 0 Comments: 6
Question Number 85601 Answers: 0 Comments: 2
$$\int\frac{\mathrm{4u}}{\mathrm{4u}^{\mathrm{2}} −\mathrm{4u}+\mathrm{1}}\mathrm{du} \\ $$
Question Number 85600 Answers: 1 Comments: 3
$$\int\frac{{x}^{\mathrm{2}} }{\sqrt{\mathrm{1}+{x}^{\mathrm{2}} }}\:{dx} \\ $$
Question Number 85596 Answers: 1 Comments: 1
$$\int\frac{\sqrt{{x}+\mathrm{1}}−\mathrm{1}}{\sqrt{{x}−\mathrm{1}}+\mathrm{1}}\:{dx} \\ $$
Question Number 85583 Answers: 0 Comments: 0
Question Number 85580 Answers: 0 Comments: 0
$$\boldsymbol{\mathrm{Solve}}: \\ $$$$\:\left(\mathrm{D}^{\mathrm{2}} +\mathrm{2D}+\mathrm{1}\right)\mathrm{y}=\:\mathrm{x}\:\mathrm{cos}\:\mathrm{x} \\ $$$$ \\ $$
Question Number 85582 Answers: 0 Comments: 1
$$\mathrm{cos}\:\left(\frac{\pi}{\mathrm{9}}\right)+\mathrm{cos}\:\left(\frac{\mathrm{2}\pi}{\mathrm{9}}\right)+\mathrm{cos}\:\left(\frac{\mathrm{4}\pi}{\mathrm{9}}\right)= \\ $$
Question Number 85568 Answers: 4 Comments: 2
$$\int\underset{\mathrm{0}} {\overset{\mathrm{2}\pi} {\:}}\:\frac{\mathrm{dx}}{\sqrt{\mathrm{2}}−\mathrm{cos}\:\mathrm{x}} \\ $$
Question Number 85557 Answers: 0 Comments: 3
$${x}\:\:=\:\:\sqrt{\mathrm{1}+\:\sqrt{\mathrm{5}+\:\sqrt{\mathrm{11}+\:\sqrt{\mathrm{19}+...}}}} \\ $$$${x}\:\:=\:\:\:? \\ $$
Question Number 85555 Answers: 1 Comments: 0
$$\mathrm{2}{x}^{\mathrm{2}} +\mathrm{5}{x}+\mathrm{7}=\mathrm{0} \\ $$
Question Number 85554 Answers: 0 Comments: 1
Question Number 85551 Answers: 0 Comments: 1
$$\int\:\frac{\mathrm{dx}}{\mathrm{x}^{\mathrm{2}} \left(\mathrm{x}^{\mathrm{4}} +\mathrm{1}\right)^{\frac{\mathrm{3}}{\mathrm{4}}} } \\ $$
Question Number 85546 Answers: 0 Comments: 1
Question Number 85542 Answers: 1 Comments: 4
Question Number 85540 Answers: 1 Comments: 0
$${find}\:{the}\:{range} \\ $$$${y}=\frac{{x}+\left[{x}\right]}{\mathrm{1}−\left[{x}\right]+{x}} \\ $$
Question Number 85535 Answers: 0 Comments: 0
Question Number 85534 Answers: 1 Comments: 2
Question Number 85532 Answers: 1 Comments: 0
$${Find}\:{the}\:{term}\:{independent}\:{of}\:\boldsymbol{\mathrm{x}}\:{in}\:{the}\:{expression}\:{of}\:\left(\mathrm{2}{x}−\frac{\mathrm{1}}{\mathrm{2}{x}}\right)^{\mathrm{9}} \\ $$
Question Number 85523 Answers: 1 Comments: 1
Question Number 85589 Answers: 0 Comments: 0
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