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IntegrationQuestion and Answers: Page 217

Question Number 72017 Answers: 0 Comments: 0

find ∫ ((x+(√(4+x^2 )))/(x−(√(4+3x^2 ))))dx

$${find}\:\int\:\:\frac{{x}+\sqrt{\mathrm{4}+{x}^{\mathrm{2}} }}{{x}−\sqrt{\mathrm{4}+\mathrm{3}{x}^{\mathrm{2}} }}{dx} \\ $$

Question Number 72016 Answers: 1 Comments: 2

find U_n =∫_0 ^∞ ((cos(nx))/((3+nx^2 )^2 ))dx with n integr

$${find}\:{U}_{{n}} =\int_{\mathrm{0}} ^{\infty} \:\:\:\frac{{cos}\left({nx}\right)}{\left(\mathrm{3}+{nx}^{\mathrm{2}} \right)^{\mathrm{2}} }{dx}\:\:{with}\:{n}\:{integr} \\ $$

Question Number 72015 Answers: 0 Comments: 1

find ∫ ((arctan(x−(1/x)))/(x^2 +1))dx

$${find}\:\int\:\:\frac{{arctan}\left({x}−\frac{\mathrm{1}}{{x}}\right)}{{x}^{\mathrm{2}} \:+\mathrm{1}}{dx} \\ $$

Question Number 72012 Answers: 0 Comments: 1

find f(α) =∫_0 ^∞ ((arctan(αx))/((x^2 +3)^2 ))dx with α real.

$${find}\:{f}\left(\alpha\right)\:=\int_{\mathrm{0}} ^{\infty} \:\:\frac{{arctan}\left(\alpha{x}\right)}{\left({x}^{\mathrm{2}} +\mathrm{3}\right)^{\mathrm{2}} }{dx}\:\:{with}\:\alpha\:{real}. \\ $$

Question Number 72011 Answers: 1 Comments: 1

calculate ∫_0 ^∞ ((ln(3+x^2 ))/((x^2 +1)^2 ))dx

$${calculate}\:\int_{\mathrm{0}} ^{\infty} \:\:\frac{{ln}\left(\mathrm{3}+{x}^{\mathrm{2}} \right)}{\left({x}^{\mathrm{2}} +\mathrm{1}\right)^{\mathrm{2}} }{dx} \\ $$

Question Number 71921 Answers: 0 Comments: 0

Question Number 72062 Answers: 1 Comments: 2

Question Number 71904 Answers: 0 Comments: 0

Question Number 71864 Answers: 1 Comments: 2

Draw the graph of : x=∣y∣ (√(1−y^2 ))

$${Draw}\:{the}\:{graph}\:{of}\:: \\ $$$${x}=\mid{y}\mid\:\sqrt{\mathrm{1}−{y}^{\mathrm{2}} } \\ $$

Question Number 71850 Answers: 2 Comments: 0

∫ln(x^x^x .e^x^x )dx=?

$$\int\mathrm{ln}\left(\mathrm{x}^{\mathrm{x}^{\mathrm{x}} } .\mathrm{e}^{\mathrm{x}^{\mathrm{x}} } \right)\mathrm{dx}=? \\ $$

Question Number 71831 Answers: 1 Comments: 2

Question Number 71816 Answers: 1 Comments: 0

suppose that f is continuous and differentiable in (a,b) if f′(x) =0 ,∀ x∈(a,b) then show that f is constant on [a,b].

$${suppose}\:{that}\:{f}\:{is}\:{continuous}\:{and}\:{differentiable}\:{in}\:\left({a},{b}\right)\:{if}\:{f}'\left({x}\right)\:=\mathrm{0}\:,\forall\:{x}\in\left({a},{b}\right)\:{then}\:{show}\:{that}\:{f}\:{is}\:{constant}\:{on}\:\left[{a},{b}\right]. \\ $$

Question Number 71814 Answers: 1 Comments: 2

∫(1/(1+cot x))dx

$$\int\frac{\mathrm{1}}{\mathrm{1}+\mathrm{cot}\:{x}}{dx} \\ $$

Question Number 71813 Answers: 0 Comments: 0

1)calculate F(a)=∫_0 ^(π/4) arctan(1+a cosx)dx 2)find the valeur of ∫_0 ^(π/4) arctan(1+(√2)cosx)dx

$$\left.\mathrm{1}\right){calculate}\:{F}\left({a}\right)=\int_{\mathrm{0}} ^{\frac{\pi}{\mathrm{4}}} {arctan}\left(\mathrm{1}+{a}\:{cosx}\right){dx} \\ $$$$\left.\mathrm{2}\right){find}\:{the}\:{valeur}\:{of}\:\:\int_{\mathrm{0}} ^{\frac{\pi}{\mathrm{4}}} \:{arctan}\left(\mathrm{1}+\sqrt{\mathrm{2}}{cosx}\right){dx} \\ $$

Question Number 71802 Answers: 1 Comments: 1

find ∫ ((x^2 −1)/((x+3)^2 (x^3 −5x+4)))dx

$${find}\:\int\:\:\:\frac{{x}^{\mathrm{2}} −\mathrm{1}}{\left({x}+\mathrm{3}\right)^{\mathrm{2}} \left({x}^{\mathrm{3}} −\mathrm{5}{x}+\mathrm{4}\right)}{dx} \\ $$

Question Number 71801 Answers: 0 Comments: 0

find I_n =∫_0 ^1 x^n (√(1+x^2 ))dx with n integr natural

$${find}\:\:{I}_{{n}} =\int_{\mathrm{0}} ^{\mathrm{1}} {x}^{{n}} \sqrt{\mathrm{1}+{x}^{\mathrm{2}} }{dx}\:\:{with}\:{n}\:{integr}\:{natural} \\ $$

Question Number 71799 Answers: 2 Comments: 0

Question Number 71665 Answers: 1 Comments: 0

calculate ∫_0 ^∞ (dx/((x+1)^2 ((√(x^2 +4)))))

$${calculate}\:\int_{\mathrm{0}} ^{\infty} \:\:\frac{{dx}}{\left({x}+\mathrm{1}\right)^{\mathrm{2}} \left(\sqrt{{x}^{\mathrm{2}} +\mathrm{4}}\right)} \\ $$

Question Number 71663 Answers: 1 Comments: 1

calculate A_n =∫_0 ^∞ (dx/((x^2 +1)(x^2 +2)....(x^2 +n))) with n integr and n≥1

$${calculate}\:{A}_{{n}} =\int_{\mathrm{0}} ^{\infty} \:\frac{{dx}}{\left({x}^{\mathrm{2}} +\mathrm{1}\right)\left({x}^{\mathrm{2}} +\mathrm{2}\right)....\left({x}^{\mathrm{2}} \:+{n}\right)} \\ $$$${with}\:{n}\:{integr}\:{and}\:{n}\geqslant\mathrm{1} \\ $$

Question Number 71499 Answers: 1 Comments: 1

Question Number 71490 Answers: 2 Comments: 2

Question Number 71314 Answers: 2 Comments: 1

find ∫_(−1) ^1 ln((√(1+x))+(√(1−x)))dx

$${find}\:\int_{−\mathrm{1}} ^{\mathrm{1}} {ln}\left(\sqrt{\mathrm{1}+{x}}+\sqrt{\mathrm{1}−{x}}\right){dx} \\ $$

Question Number 71239 Answers: 2 Comments: 3

∫(1/(2cosx−5sinx−3))dx

$$\int\frac{\mathrm{1}}{\mathrm{2cosx}−\mathrm{5sinx}−\mathrm{3}}\mathrm{dx} \\ $$

Question Number 71220 Answers: 0 Comments: 0

Question Number 71197 Answers: 0 Comments: 0

Question Number 71175 Answers: 1 Comments: 3

∫(1/(x^2 +2016x))dx

$$\int\frac{\mathrm{1}}{\mathrm{x}^{\mathrm{2}} +\mathrm{2016x}}\mathrm{dx} \\ $$

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