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AllQuestion and Answers: Page 325

Question Number 186253 Answers: 1 Comments: 1

Question Number 186249 Answers: 0 Comments: 0

Question Number 186248 Answers: 0 Comments: 0

Question Number 186247 Answers: 0 Comments: 0

Question Number 186246 Answers: 1 Comments: 0

Question Number 186241 Answers: 2 Comments: 3

x+(1/x)=((−1+(√5))/2) x?

$${x}+\frac{\mathrm{1}}{{x}}=\frac{−\mathrm{1}+\sqrt{\mathrm{5}}}{\mathrm{2}} \\ $$$${x}? \\ $$

Question Number 186236 Answers: 1 Comments: 0

Question Number 186352 Answers: 1 Comments: 0

∫_1 ^( 2) ((tan^(−1) (x) + 2)/x^2 ) dx

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

Question Number 186232 Answers: 1 Comments: 0

1+(x/(1+(x/(1+(x/∙_∙_∙ )))))=5 x=?

$$\mathrm{1}+\frac{{x}}{\mathrm{1}+\frac{{x}}{\mathrm{1}+\frac{{x}}{\centerdot_{\centerdot_{\centerdot} } }}}=\mathrm{5}\:\:\:\:\:\:\:\:\:{x}=? \\ $$

Question Number 186230 Answers: 2 Comments: 0

Question Number 186231 Answers: 0 Comments: 0

Question Number 186223 Answers: 1 Comments: 0

∫_o ^(+oo) e^(−E(x)dx)

$$\int_{{o}} ^{+{oo}} {e}^{−{E}\left({x}\right){dx}} \\ $$

Question Number 186214 Answers: 0 Comments: 12

if S_a =cos(a)+sin(x+a) then ∫(S_1 /S_2 )−((x+S_1 )/(x−S_3 ))dx=?

$${if}\:{S}_{{a}} =\mathrm{cos}\left({a}\right)+\mathrm{sin}\left({x}+{a}\right) \\ $$$${then}\:\int\frac{{S}_{\mathrm{1}} }{{S}_{\mathrm{2}} }−\frac{{x}+{S}_{\mathrm{1}} }{{x}−{S}_{\mathrm{3}} }{dx}=? \\ $$

Question Number 186198 Answers: 1 Comments: 0

∫^3 _2 ((x^2 − 1)/(1 + ^x^2 (√(2 ln(x))))) dx

$$ \\ $$$$\:\:\:\:\:\underset{\mathrm{2}} {\int}^{\mathrm{3}} \:\:\:\frac{\boldsymbol{{x}}^{\mathrm{2}} \:\:−\:\:\mathrm{1}}{\mathrm{1}\:\:\:+\:\:\:^{{x}^{\mathrm{2}} } \sqrt{\mathrm{2}\:\boldsymbol{{ln}}\left(\boldsymbol{{x}}\right)}}\:\:\:\boldsymbol{{dx}}\:\:\:\: \\ $$$$ \\ $$

Question Number 186196 Answers: 3 Comments: 2

∫_1 ^2 (((√(1 )) + cos (x))/( (√1) − cos (x))) dx

$$ \\ $$$$\:\:\:\:\:\:\:\underset{\mathrm{1}} {\overset{\mathrm{2}} {\int}}\:\:\frac{\sqrt{\mathrm{1}\:}\:\:+\:\:\boldsymbol{{cos}}\:\left(\boldsymbol{{x}}\right)}{\:\sqrt{\mathrm{1}}\:\:\:−\:\:\boldsymbol{{cos}}\:\left(\boldsymbol{{x}}\right)}\:\:\boldsymbol{{dx}}\:\:\:\:\:\: \\ $$$$ \\ $$

Question Number 186195 Answers: 1 Comments: 0

∫_1 ^2 ((1/2 ∙(x^2 ) )/(x (√(x^2 + 2)))) dx

$$ \\ $$$$\:\:\:\:\underset{\mathrm{1}} {\overset{\mathrm{2}} {\int}}\:\:\:\frac{\mathrm{1}/\mathrm{2}\:\centerdot\left(\boldsymbol{{x}}^{\mathrm{2}} \right)\:}{\boldsymbol{{x}}\:\sqrt{\boldsymbol{{x}}^{\mathrm{2}} \:+\:\:\mathrm{2}}}\:\:\boldsymbol{{dx}}\:\:\:\: \\ $$

Question Number 186194 Answers: 1 Comments: 2

∫_2 ^4 ((2x^2 − 1)/(1 + (√x^2 ) − 2)) dx

$$ \\ $$$$\:\:\:\:\:\:\underset{\mathrm{2}} {\overset{\mathrm{4}} {\int}}\:\:\frac{\mathrm{2}\boldsymbol{{x}}^{\mathrm{2}} \:−\:\mathrm{1}}{\mathrm{1}\:+\:\:\sqrt{\boldsymbol{{x}}^{\mathrm{2}} }\:\:−\:\:\mathrm{2}}\:\:\boldsymbol{{dx}}\:\:\:\: \\ $$$$ \\ $$

Question Number 186193 Answers: 2 Comments: 0

∫_0 ^1 ((sin (x))/(1 + cos(x))) dx

$$ \\ $$$$\:\:\:\:\:\:\:\underset{\mathrm{0}} {\overset{\mathrm{1}} {\int}}\:\:\:\frac{\boldsymbol{{sin}}\:\left(\boldsymbol{{x}}\right)}{\mathrm{1}\:\:+\:\:\boldsymbol{{cos}}\left(\boldsymbol{{x}}\right)}\:\:\boldsymbol{{dx}} \\ $$

Question Number 186192 Answers: 1 Comments: 0

My old problem ∫ e^(tan x) dx

$$ \\ $$$$\:\:\:\:\:\:\:\boldsymbol{{My}}\:\boldsymbol{{old}}\:\boldsymbol{{problem}} \\ $$$$\:\:\:\int\:\:\boldsymbol{{e}}^{\boldsymbol{{tan}}\:\boldsymbol{{x}}} \:\:\boldsymbol{{dx}} \\ $$

Question Number 186190 Answers: 0 Comments: 1

My old problem.. ∫_0 ^(+∞) ((tan^(−1) (1−cos(x)))/x^2 ) dx

$$ \\ $$$$\:\:\:\:\boldsymbol{{My}}\:\boldsymbol{{old}}\:\boldsymbol{{problem}}.. \\ $$$$\:\:\:\:\:\:\:\:\:\underset{\mathrm{0}} {\overset{+\infty} {\int}}\:\:\frac{\mathrm{tan}^{−\mathrm{1}} \left(\mathrm{1}−\boldsymbol{{cos}}\left(\boldsymbol{{x}}\right)\right)}{\boldsymbol{{x}}^{\mathrm{2}} }\:\:\boldsymbol{{dx}}\:\:\: \\ $$$$ \\ $$

Question Number 186188 Answers: 0 Comments: 0

Prove that Π_(k=1) ^p tan(((kπ)/(2p+1)))=(√(2p+1))

$$\mathrm{Prove}\:\mathrm{that}\:\underset{\mathrm{k}=\mathrm{1}} {\overset{\mathrm{p}} {\prod}}\mathrm{tan}\left(\frac{\mathrm{k}\pi}{\mathrm{2p}+\mathrm{1}}\right)=\sqrt{\mathrm{2p}+\mathrm{1}} \\ $$

Question Number 186187 Answers: 0 Comments: 4

Σ_(k=0) ^(+∞) (−1)^k (_(2k) ^n )=?

$$\underset{\mathrm{k}=\mathrm{0}} {\overset{+\infty} {\sum}}\left(−\mathrm{1}\right)^{\mathrm{k}} \left(_{\mathrm{2k}} ^{\mathrm{n}} \right)=? \\ $$

Question Number 186181 Answers: 1 Comments: 0

∫_0 ^π (√(1+cos^2 x)) dx =?

$$\:\:\underset{\mathrm{0}} {\overset{\pi} {\int}}\:\sqrt{\mathrm{1}+\mathrm{cos}\:^{\mathrm{2}} {x}}\:{dx}\:=? \\ $$

Question Number 186172 Answers: 2 Comments: 0

Question Number 186171 Answers: 1 Comments: 0

[so easy] ∫ cos^2 (4x) + sin^4 (2x) dx

$$ \\ $$$$\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\left[\boldsymbol{{so}}\:\boldsymbol{{easy}}\right] \\ $$$$\:\:\:\:\:\:\:\int\:\boldsymbol{{cos}}^{\mathrm{2}} \:\left(\mathrm{4}\boldsymbol{{x}}\right)\:+\:\boldsymbol{{sin}}^{\mathrm{4}} \:\left(\mathrm{2}\boldsymbol{{x}}\right)\:\boldsymbol{{dx}}\:\:\: \\ $$$$ \\ $$

Question Number 186170 Answers: 1 Comments: 0

∫_(−2) ^2 ((tan^(−1) ( 2 − cos (x)) )/(2 + x^2 )) dx

$$ \\ $$$$\:\:\:\:\:\:\underset{−\mathrm{2}} {\overset{\mathrm{2}} {\int}}\:\:\:\:\frac{\boldsymbol{{tan}}^{−\mathrm{1}} \:\left(\:\mathrm{2}\:−\:\boldsymbol{{cos}}\:\left(\boldsymbol{{x}}\right)\right)\:\:\:\:}{\mathrm{2}\:+\:\boldsymbol{{x}}^{\mathrm{2}} }\:\:\boldsymbol{{dx}} \\ $$$$ \\ $$

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