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IntegrationQuestion and Answers: Page 22

Question Number 201546 Answers: 2 Comments: 4

∫Sin(Inx)dx

$$\:\:\:\int\boldsymbol{{Sin}}\left(\boldsymbol{{Inx}}\right)\boldsymbol{{dx}} \\ $$

Question Number 201510 Answers: 1 Comments: 0

Question Number 201509 Answers: 1 Comments: 0

Question Number 201452 Answers: 2 Comments: 0

Question Number 201445 Answers: 0 Comments: 0

Question Number 201347 Answers: 1 Comments: 0

Question Number 201341 Answers: 2 Comments: 0

if a>0 and m≥0 ∫_0 ^∞ ((cos(mx))/((x^2 +a^2 )^2 ))dx=?

$${if}\:{a}>\mathrm{0}\:\:{and}\:\:{m}\geqslant\mathrm{0} \\ $$$$\int_{\mathrm{0}} ^{\infty} \frac{{cos}\left({mx}\right)}{\left({x}^{\mathrm{2}} +{a}^{\mathrm{2}} \right)^{\mathrm{2}} }{dx}=? \\ $$

Question Number 201456 Answers: 1 Comments: 0

Question Number 201281 Answers: 0 Comments: 0

Question Number 201267 Answers: 0 Comments: 1

find ∫_0 ^1 (dx/((1+x)^(3/2) +(x−1)^(3/2) ))

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

Question Number 201266 Answers: 2 Comments: 0

calculate ∫_1 ^∞ (dx/( (√(1+x^3 ))))

$${calculate}\:\int_{\mathrm{1}} ^{\infty} \frac{{dx}}{\:\sqrt{\mathrm{1}+{x}^{\mathrm{3}} }} \\ $$

Question Number 201241 Answers: 0 Comments: 0

Question Number 201229 Answers: 1 Comments: 2

∫ (1/( (√(1+Inx))))dx

$$\int\:\frac{\mathrm{1}}{\:\sqrt{\mathrm{1}+\boldsymbol{{Inx}}}}\boldsymbol{{dx}} \\ $$

Question Number 201228 Answers: 0 Comments: 0

∫(√(x+(√(x+(√x))))) dx

$$\int\sqrt{\boldsymbol{{x}}+\sqrt{\boldsymbol{{x}}+\sqrt{\boldsymbol{{x}}}}}\:\boldsymbol{{dx}} \\ $$

Question Number 201227 Answers: 1 Comments: 0

∫ (((x^4 +x^7 )^(1/4) )/x^2 )dx

$$\:\int\:\frac{\left(\boldsymbol{{x}}^{\mathrm{4}} +\boldsymbol{{x}}^{\mathrm{7}} \right)^{\frac{\mathrm{1}}{\mathrm{4}}} }{\boldsymbol{{x}}^{\mathrm{2}} }\boldsymbol{{dx}} \\ $$

Question Number 201224 Answers: 2 Comments: 0

∫ (1/( (√(1+sinx))))dx

$$\int\:\frac{\mathrm{1}}{\:\sqrt{\mathrm{1}+\boldsymbol{{sinx}}}}\boldsymbol{{dx}} \\ $$

Question Number 201223 Answers: 1 Comments: 0

∫(√(1+(√(1+x)))) dx

$$\int\sqrt{\mathrm{1}+\sqrt{\mathrm{1}+\boldsymbol{{x}}}}\:\boldsymbol{{dx}} \\ $$

Question Number 201222 Answers: 1 Comments: 0

∫ (x^6 +x^9 )^(1/6) dx

$$\:\int\:\left(\boldsymbol{{x}}^{\mathrm{6}} +\boldsymbol{{x}}^{\mathrm{9}} \right)^{\frac{\mathrm{1}}{\mathrm{6}}} \boldsymbol{{dx}} \\ $$

Question Number 201172 Answers: 1 Comments: 0

Question Number 201110 Answers: 1 Comments: 0

∫(1/( (√((x−a)^3 ))+(√((x+a)^3 ))))dx

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

Question Number 201184 Answers: 1 Comments: 0

Question Number 201044 Answers: 2 Comments: 0

Ω = ∫_0 ^( 1) ∫_0 ^( 1) (x−y )^2 sin^( 2) ( x+y )dxdy=?

$$ \\ $$$$\:\:\:\:\Omega\:=\:\int_{\mathrm{0}} ^{\:\mathrm{1}} \int_{\mathrm{0}} ^{\:\mathrm{1}} \left({x}−{y}\:\right)^{\mathrm{2}} {sin}^{\:\mathrm{2}} \:\left(\:{x}+{y}\:\right){dxdy}=? \\ $$

Question Number 201016 Answers: 0 Comments: 0

Question Number 201011 Answers: 0 Comments: 0

Prove that ∫_0 ^∞ ((2arctan((t/x)))/(e^(2𝛑t) −1))dt=In𝚪(x)−xIn(x)+x−(1/2)In(((2𝛑)/x)) Michael faraday

$$\boldsymbol{{Prove}}\:\boldsymbol{{that}} \\ $$$$\int_{\mathrm{0}} ^{\infty} \:\frac{\mathrm{2}\boldsymbol{{arctan}}\left(\frac{\boldsymbol{{t}}}{\boldsymbol{{x}}}\right)}{\boldsymbol{{e}}^{\mathrm{2}\boldsymbol{\pi{t}}} −\mathrm{1}}\boldsymbol{{dt}}=\boldsymbol{{In}\Gamma}\left(\boldsymbol{{x}}\right)−\boldsymbol{{xIn}}\left(\boldsymbol{{x}}\right)+\boldsymbol{{x}}−\frac{\mathrm{1}}{\mathrm{2}}\boldsymbol{{In}}\left(\frac{\mathrm{2}\boldsymbol{\pi}}{\boldsymbol{{x}}}\right) \\ $$$$\boldsymbol{{Michael}}\:\boldsymbol{{faraday}} \\ $$

Question Number 200933 Answers: 0 Comments: 0

∫coth (ln [(√(tanh (ln ((√(sec^(−1) (x)^(1/4) )))))) ])

$$ \\ $$$$\int\mathrm{coth}\:\left(\mathrm{ln}\:\left[\sqrt{\mathrm{tanh}\:\left(\mathrm{ln}\:\left(\sqrt{\mathrm{sec}^{−\mathrm{1}} \:\:\sqrt[{\mathrm{4}}]{{x}}\:\:}\right)\right)}\:\right]\right) \\ $$$$ \\ $$$$ \\ $$

Question Number 200923 Answers: 0 Comments: 0

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