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AllQuestion and Answers: Page 319

Question Number 186925 Answers: 0 Comments: 1

Question Number 186921 Answers: 0 Comments: 0

Question Number 186912 Answers: 0 Comments: 2

Question Number 186911 Answers: 1 Comments: 0

∫_0 ^∞ (1/(1+a^x +a^(x/2) ))dx = (1/(ln a))[ln 3−(π/(3(√3)))]

$$ \\ $$$$\int_{\mathrm{0}} ^{\infty} \frac{\mathrm{1}}{\mathrm{1}+{a}^{{x}} +{a}^{\frac{{x}}{\mathrm{2}}} }{dx}\:=\:\frac{\mathrm{1}}{\mathrm{ln}\:{a}}\left[\mathrm{ln}\:\mathrm{3}−\frac{\pi}{\mathrm{3}\sqrt{\mathrm{3}}}\right] \\ $$

Question Number 186910 Answers: 1 Comments: 0

∫_0 ^a (√((cos 2x−cos 2a)/(cos 2x+1))) dx=(π/2)(1−cos a)

$$ \\ $$$$\:\:\:\:\:\:\int_{\mathrm{0}} ^{{a}} \sqrt{\frac{\mathrm{cos}\:\mathrm{2}{x}−\mathrm{cos}\:\mathrm{2}{a}}{\mathrm{cos}\:\mathrm{2}{x}+\mathrm{1}}}\:{dx}=\frac{\pi}{\mathrm{2}}\left(\mathrm{1}−\mathrm{cos}\:{a}\right) \\ $$$$ \\ $$$$ \\ $$$$ \\ $$

Question Number 186967 Answers: 1 Comments: 1

Question Number 186966 Answers: 1 Comments: 2

Question Number 186965 Answers: 1 Comments: 1

Question Number 186964 Answers: 1 Comments: 2

Question Number 186963 Answers: 1 Comments: 1

Question Number 186962 Answers: 1 Comments: 0

Question Number 186976 Answers: 1 Comments: 1

Question Number 186901 Answers: 1 Comments: 0

Question Number 186973 Answers: 0 Comments: 1

∫5x

$$\int\mathrm{5}{x} \\ $$

Question Number 186884 Answers: 1 Comments: 6

Question Number 186883 Answers: 2 Comments: 0

Question Number 186882 Answers: 0 Comments: 0

Question Number 186870 Answers: 4 Comments: 1

Question Number 186868 Answers: 2 Comments: 1

Question Number 186867 Answers: 2 Comments: 0

Question Number 186863 Answers: 0 Comments: 0

Question Number 186864 Answers: 2 Comments: 0

if AB,BA and BB three tow digits natural numbers if (((AB+BA))/(BB))=4 then find the maximum volue of (A+B)=?

$${if}\:\:{AB},{BA}\:{and}\:{BB}\:\:{three}\:\:{tow}\:{digits}\:{natural} \\ $$$${numbers}\:{if}\:\:\frac{\left({AB}+{BA}\right)}{{BB}}=\mathrm{4} \\ $$$${then}\:{find}\:{the}\:{maximum}\:{volue}\:{of} \\ $$$$\left({A}+{B}\right)=? \\ $$

Question Number 193967 Answers: 1 Comments: 0

Question Number 186858 Answers: 0 Comments: 0

Discuss according to the value of the parametre α∈R the convergence of the improper integral ∫_0 ^(+∞) x^α ln(x+e^(αx) )dx

$${Discuss}\:{according}\:{to}\:{the}\:{value}\:{of}\:{the}\:{parametre} \\ $$$$\alpha\in\mathbb{R}\:{the}\:{convergence}\:{of}\:{the}\:{improper}\:{integral} \\ $$$$\int_{\mathrm{0}} ^{+\infty} {x}^{\alpha} {ln}\left({x}+{e}^{\alpha{x}} \right){dx} \\ $$

Question Number 186856 Answers: 0 Comments: 0

∫ (((√(x+3))+(√(x+2)))/( (√(x+3))+(√(x−2)))) dx =?

$$\int\:\frac{\sqrt{{x}+\mathrm{3}}+\sqrt{{x}+\mathrm{2}}}{\:\sqrt{{x}+\mathrm{3}}+\sqrt{{x}−\mathrm{2}}}\:{dx}\:=? \\ $$

Question Number 186854 Answers: 1 Comments: 0

∫_0 ^( R) ((Rcosx)/(l−Rcosx))dx=?

$$\int_{\mathrm{0}} ^{\:{R}} \frac{{Rcosx}}{{l}−{Rcosx}}{dx}=? \\ $$

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