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IntegrationQuestion and Answers: Page 194

Question Number 77447    Answers: 1   Comments: 0

∫ tan(x) tan(2x) tan(3x) dx

$$\int\:\mathrm{tan}\left(\mathrm{x}\right)\:\mathrm{tan}\left(\mathrm{2x}\right)\:\mathrm{tan}\left(\mathrm{3x}\right)\:\mathrm{dx} \\ $$

Question Number 77424    Answers: 0   Comments: 0

∫_0 ^∞ e^((e^x −1)^t (A)) dx A and t are constant

$$\int_{\mathrm{0}} ^{\infty} {e}^{\left({e}^{{x}} −\mathrm{1}\right)^{{t}} \:\left({A}\right)} \:{dx} \\ $$$${A}\:{and}\:{t}\:{are}\:{constant} \\ $$

Question Number 77422    Answers: 1   Comments: 1

can solve ∫ (dx/(x^(17) −1)) via elementary calculus?

$$\mathrm{can}\:\mathrm{solve}\:\int\:\frac{\mathrm{dx}}{\mathrm{x}^{\mathrm{17}} −\mathrm{1}}\:\mathrm{via}\: \\ $$$$\mathrm{elementary}\:\mathrm{calculus}? \\ $$

Question Number 77335    Answers: 1   Comments: 4

Question Number 77323    Answers: 0   Comments: 2

Question Number 77290    Answers: 2   Comments: 3

∫ (√(x^3 + x^4 )) dx

$$\int\:\sqrt{\mathrm{x}^{\mathrm{3}} \:+\:\mathrm{x}^{\mathrm{4}} }\:\:\mathrm{dx} \\ $$

Question Number 77269    Answers: 0   Comments: 1

what is ∫ (1/(tan^3 (x^2 −1))) dx ?

$${what}\:{is}\:\int\:\frac{\mathrm{1}}{\mathrm{tan}\:^{\mathrm{3}} \left({x}^{\mathrm{2}} −\mathrm{1}\right)}\:{dx}\:? \\ $$

Question Number 77242    Answers: 1   Comments: 3

prove that ∫_0 ^a (√(2+(a/x)−2(√(a/x)) ))dx=a[(1/(√2))ln((√2)+1)+1]

$${prove}\:{that} \\ $$$$\:\int_{\mathrm{0}} ^{{a}} \sqrt{\mathrm{2}+\frac{{a}}{{x}}−\mathrm{2}\sqrt{\frac{{a}}{{x}}}\:}{dx}={a}\left[\frac{\mathrm{1}}{\sqrt{\mathrm{2}}}{ln}\left(\sqrt{\mathrm{2}}+\mathrm{1}\right)+\mathrm{1}\right] \\ $$

Question Number 77221    Answers: 2   Comments: 0

∫ (((√(2+x)) dx)/(√x^5 )) = ?

$$\int\:\frac{\sqrt{\mathrm{2}+{x}}\:{dx}}{\sqrt{{x}^{\mathrm{5}} }}\:=\:? \\ $$

Question Number 77158    Answers: 0   Comments: 4

∫_(−2) ^( 2) (x^3 cos(x/2) + (1/2))(√(4 − x^2 )) dx

$$\int_{−\mathrm{2}} ^{\:\mathrm{2}} \:\left(\mathrm{x}^{\mathrm{3}} \:\mathrm{cos}\frac{\mathrm{x}}{\mathrm{2}}\:+\:\frac{\mathrm{1}}{\mathrm{2}}\right)\sqrt{\mathrm{4}\:−\:\mathrm{x}^{\mathrm{2}} }\:\:\mathrm{dx} \\ $$

Question Number 77103    Answers: 1   Comments: 1

Question Number 77089    Answers: 0   Comments: 2

Cheap ⇊ ∫(√(x/(√(x/(√(x/(...)))))))dx

$$\boldsymbol{{Cheap}}\:\downdownarrows \\ $$$$\int\sqrt{\frac{\boldsymbol{{x}}}{\sqrt{\frac{\boldsymbol{{x}}}{\sqrt{\frac{\boldsymbol{{x}}}{...}}}}}}\boldsymbol{{dx}} \\ $$$$ \\ $$$$ \\ $$

Question Number 77087    Answers: 1   Comments: 1

∫_0 ^(a/2) x^2 (a^2 −x^2 )^((−3)/2) dx Help!!!

$$\int_{\mathrm{0}} ^{\frac{\boldsymbol{{a}}}{\mathrm{2}}} \boldsymbol{{x}}^{\mathrm{2}} \left(\boldsymbol{{a}}^{\mathrm{2}} −\boldsymbol{{x}}^{\mathrm{2}} \right)^{\frac{−\mathrm{3}}{\mathrm{2}}} \boldsymbol{{dx}} \\ $$$$\boldsymbol{{Help}}!!! \\ $$$$ \\ $$

Question Number 77086    Answers: 1   Comments: 2

∫_0 ^1 xtan^(−1) xdx

$$\int_{\mathrm{0}} ^{\mathrm{1}} {xtan}^{−\mathrm{1}} {xdx} \\ $$$$ \\ $$

Question Number 77036    Answers: 0   Comments: 12

Question Number 77002    Answers: 2   Comments: 2

calculate ∫ (dt/(cos (2t+a)cos (2t−a)))

$$ \\ $$$${calculate}\:\int\:\frac{{dt}}{\mathrm{cos}\:\left(\mathrm{2}{t}+{a}\right)\mathrm{cos}\:\left(\mathrm{2}{t}−{a}\right)} \\ $$

Question Number 76958    Answers: 1   Comments: 1

∫ln e^y dy

$$\int{ln}\:{e}^{{y}} {dy} \\ $$

Question Number 76956    Answers: 1   Comments: 0

∫_( 0) ^( a) (dx/(√((a+sinx)(a+cosx)))) =? [a∈R^+ ,test for: a=1]

$$\underset{\:\:\mathrm{0}} {\overset{\:\:\:\:\:\:\:\:\boldsymbol{\mathrm{a}}} {\int}}\:\:\:\frac{\boldsymbol{\mathrm{dx}}}{\sqrt{\left(\boldsymbol{\mathrm{a}}+\boldsymbol{\mathrm{sinx}}\right)\left(\boldsymbol{\mathrm{a}}+\boldsymbol{\mathrm{cosx}}\right)}}\:=? \\ $$$$\left[\boldsymbol{\mathrm{a}}\in\boldsymbol{\mathrm{R}}^{+} ,\boldsymbol{\mathrm{test}}\:\boldsymbol{\mathrm{for}}:\:\:\boldsymbol{\mathrm{a}}=\mathrm{1}\right] \\ $$

Question Number 76955    Answers: 0   Comments: 0

∫ (x^p /(√(1±x^q ))) dx=? [p+q=2n∈N,p<q]

$$\int\:\:\frac{\boldsymbol{\mathrm{x}}^{\boldsymbol{\mathrm{p}}} }{\sqrt{\mathrm{1}\pm\boldsymbol{\mathrm{x}}^{\boldsymbol{\mathrm{q}}} }}\:\boldsymbol{\mathrm{dx}}=?\:\:\:\:\left[\boldsymbol{\mathrm{p}}+\boldsymbol{\mathrm{q}}=\mathrm{2}\boldsymbol{\mathrm{n}}\in\boldsymbol{\mathrm{N}},\boldsymbol{\mathrm{p}}<\boldsymbol{\mathrm{q}}\right] \\ $$

Question Number 76954    Answers: 0   Comments: 0

∫ (dx/(√(1+sinx.sin2x))) =?

$$\int\:\:\:\frac{\boldsymbol{\mathrm{dx}}}{\sqrt{\mathrm{1}+\boldsymbol{\mathrm{sinx}}.\boldsymbol{\mathrm{sin}}\mathrm{2}\boldsymbol{\mathrm{x}}}}\:\:=? \\ $$

Question Number 76920    Answers: 0   Comments: 1

how can i solve ∫ ((sin x dx)/(x^2 e^x )) ? can using elementary calculus?

$${how}\:{can}\:{i}\:{solve}\: \\ $$$$\int\:\frac{\mathrm{sin}\:{x}\:{dx}}{{x}^{\mathrm{2}} \:{e}^{{x}} }\:?\:{can}\:{using}\:{elementary} \\ $$$${calculus}? \\ $$

Question Number 76913    Answers: 1   Comments: 0

Question Number 76910    Answers: 1   Comments: 1

Question Number 76892    Answers: 3   Comments: 0

Calculate ∫ ((√(9−x^2 ))/x^6 ) dx .

$$\mathcal{C}{alculate}\:\int\:\frac{\sqrt{\mathrm{9}−{x}^{\mathrm{2}} }}{{x}^{\mathrm{6}} }\:{dx}\:. \\ $$

Question Number 76826    Answers: 1   Comments: 0

Question Number 76808    Answers: 1   Comments: 3

∫(1/(√(x^3 +1)))dx

$$\int\frac{\mathrm{1}}{\sqrt{{x}^{\mathrm{3}} +\mathrm{1}}}{dx} \\ $$

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