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IntegrationQuestion and Answers: Page 192

Question Number 86611 Answers: 1 Comments: 0

∫_1 ^e ((ln x)/(x+1))dx

$$\int_{\mathrm{1}} ^{{e}} \frac{\mathrm{ln}\:\mathrm{x}}{\mathrm{x}+\mathrm{1}}\mathrm{dx} \\ $$

Question Number 86591 Answers: 0 Comments: 0

∫_(−1) ^1 ⌊ ∣x∣+(x)^(1/3) ⌋ dx

$$\int_{−\mathrm{1}} ^{\mathrm{1}} \lfloor\:\mid{x}\mid+\sqrt[{\mathrm{3}}]{{x}}\:\rfloor\:{dx} \\ $$

Question Number 86578 Answers: 0 Comments: 2

Question Number 86576 Answers: 0 Comments: 3

∫ ((ln (1+arc sin (x^2 )))/(sin (x^2 ))) dx ?

$$\int\:\frac{\mathrm{ln}\:\left(\mathrm{1}+\mathrm{arc}\:\mathrm{sin}\:\left(\mathrm{x}^{\mathrm{2}} \right)\right)}{\mathrm{sin}\:\left(\mathrm{x}^{\mathrm{2}} \right)}\:\mathrm{dx}\:? \\ $$

Question Number 86518 Answers: 0 Comments: 1

∫ (dx/(e^(2x) −5e^x ))

$$\int\:\:\frac{\mathrm{dx}}{\mathrm{e}^{\mathrm{2x}} −\mathrm{5e}^{\mathrm{x}} } \\ $$

Question Number 86491 Answers: 2 Comments: 1

∫ ((x^2 +1)/(x^4 +1)) dx ?

$$\int\:\:\frac{\mathrm{x}^{\mathrm{2}} +\mathrm{1}}{\mathrm{x}^{\mathrm{4}} +\mathrm{1}}\:\mathrm{dx}\:?\: \\ $$

Question Number 86484 Answers: 2 Comments: 9

∫(x^6 /(1+x^(12) ))dx

$$\int\frac{{x}^{\mathrm{6}} }{\mathrm{1}+{x}^{\mathrm{12}} }{dx} \\ $$

Question Number 86480 Answers: 0 Comments: 1

∫_0 ^∞ (x e^(1−x) −⌊x⌋e^(1−⌊x⌋) )dx

$$\int_{\mathrm{0}} ^{\infty} \left({x}\:{e}^{\mathrm{1}−{x}} \:−\lfloor{x}\rfloor{e}^{\mathrm{1}−\lfloor{x}\rfloor} \right){dx} \\ $$

Question Number 86472 Answers: 1 Comments: 0

Question Number 86447 Answers: 0 Comments: 1

Question Number 86431 Answers: 2 Comments: 0

∫(√(x−(√(x^2 +1)) )) dx

$$\int\sqrt{{x}−\sqrt{{x}^{\mathrm{2}} +\mathrm{1}}\:}\:{dx} \\ $$

Question Number 86428 Answers: 0 Comments: 2

∫ (dx/(a cos x + b sin x))?

$$\int\:\:\frac{\mathrm{dx}}{\mathrm{a}\:\mathrm{cos}\:\mathrm{x}\:+\:\mathrm{b}\:\mathrm{sin}\:\mathrm{x}}? \\ $$

Question Number 86407 Answers: 1 Comments: 1

Question Number 86405 Answers: 1 Comments: 2

Question Number 86399 Answers: 2 Comments: 3

Question Number 86397 Answers: 2 Comments: 2

∫(dx/(sin^2 (x)+tan^2 (x))) dx

$$\int\frac{{dx}}{{sin}^{\mathrm{2}} \left({x}\right)+{tan}^{\mathrm{2}} \left({x}\right)}\:{dx} \\ $$

Question Number 86375 Answers: 1 Comments: 2

calculate by complex method ∫_0 ^∞ (dx/(x^2 −x+1))

$${calculate}\:{by}\:{complex}\:{method}\:\:\int_{\mathrm{0}} ^{\infty} \:\:\:\:\frac{{dx}}{{x}^{\mathrm{2}} −{x}+\mathrm{1}} \\ $$

Question Number 86341 Answers: 0 Comments: 0

Can anyone pls check question no. 76808

$${Can}\:{anyone}\:{pls}\:{check}\: \\ $$$${question}\:{no}.\:\mathrm{76808} \\ $$

Question Number 86328 Answers: 1 Comments: 0

∫((x^2 −1)/((x^2 +1)(√(1+x^4 )))) dx

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

Question Number 86326 Answers: 0 Comments: 0

Let f a continue function acknowleding α as a fix point on [0,1].F a function such as (dF/dx)=f(x) ∀ n , u_(n+1) =((F(u_n )−F(α))/(u_n −α)) Prove that lim_(n→∞) u_n =α

$${Let}\:{f}\:{a}\:{continue}\:{function}\:{acknowleding} \\ $$$$\alpha\:{as}\:{a}\:{fix}\:{point}\:{on}\:\left[\mathrm{0},\mathrm{1}\right].{F}\:\:{a}\:{function}\:{such}\:{as}\:\frac{{dF}}{{dx}}={f}\left({x}\right) \\ $$$$\forall\:{n}\:,\:\:{u}_{{n}+\mathrm{1}} =\frac{{F}\left({u}_{{n}} \right)−{F}\left(\alpha\right)}{{u}_{{n}} −\alpha}\: \\ $$$${Prove}\:{that}\:\underset{{n}\rightarrow\infty} {\mathrm{lim}}\:{u}_{{n}} \:=\alpha \\ $$

Question Number 86324 Answers: 0 Comments: 2

∫_( 0) ^( (π/4)) ((1 )/((√(sin x)) + (√(cos x)))) dx

$$\int_{\:\mathrm{0}} ^{\:\frac{\pi}{\mathrm{4}}} \:\frac{\mathrm{1}\:}{\sqrt{\boldsymbol{\mathrm{sin}}\:\boldsymbol{\mathrm{x}}}\:\:\:+\:\:\sqrt{\boldsymbol{\mathrm{cos}}\:\boldsymbol{\mathrm{x}}}}\:\boldsymbol{\mathrm{dx}} \\ $$

Question Number 86313 Answers: 2 Comments: 2

∫_0 ^(π/2) (dx/(√(1+tan x)))

$$\underset{\mathrm{0}} {\overset{\frac{\pi}{\mathrm{2}}} {\int}}\:\frac{{dx}}{\sqrt{\mathrm{1}+\mathrm{tan}\:{x}}} \\ $$

Question Number 86302 Answers: 1 Comments: 1

∫ (dx/((x^2 +1)(√(x^2 +4)))) =?

$$\int\:\frac{{dx}}{\left({x}^{\mathrm{2}} +\mathrm{1}\right)\sqrt{{x}^{\mathrm{2}} +\mathrm{4}}}\:=? \\ $$

Question Number 86374 Answers: 0 Comments: 1

calculate bycomplex method ∫_1 ^(+∞) (dx/(1+x^2 ))

$${calculate}\:{bycomplex}\:{method}\:\:\int_{\mathrm{1}} ^{+\infty} \:\frac{{dx}}{\mathrm{1}+{x}^{\mathrm{2}} } \\ $$

Question Number 86269 Answers: 0 Comments: 1

∫((sec^2 (x))/((tan(x)−1)^4 (tan(x)−2))) dx

$$\int\frac{{sec}^{\mathrm{2}} \left({x}\right)}{\left({tan}\left({x}\right)−\mathrm{1}\right)^{\mathrm{4}} \left({tan}\left({x}\right)−\mathrm{2}\right)}\:{dx} \\ $$

Question Number 86254 Answers: 1 Comments: 0

∫ (√(x(√(x(√(x(√(x.......)))))))) dx

$$\int\:\sqrt{\mathrm{x}\sqrt{\mathrm{x}\sqrt{\mathrm{x}\sqrt{\mathrm{x}.......}}}}\:\:\:\mathrm{dx} \\ $$

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