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IntegrationQuestion and Answers: Page 167

Question Number 97153 Answers: 2 Comments: 0

Question Number 97132 Answers: 1 Comments: 1

is the formulla of sin^3 ((π/2)+x)=cos^3 x correct?

$$\mathrm{is}\:\mathrm{the}\:\mathrm{formulla}\:\mathrm{of}\:\mathrm{sin}\:^{\mathrm{3}} \left(\frac{\pi}{\mathrm{2}}+\mathrm{x}\right)=\mathrm{cos}\:^{\mathrm{3}} \mathrm{x}\:\:\:\:\mathrm{correct}? \\ $$

Question Number 97130 Answers: 1 Comments: 0

Question Number 97109 Answers: 2 Comments: 0

∫_0 ^(π/2) ((sin^3 x)/(sin^3 x+cos^3 ×))dx=?

$$\int_{\mathrm{0}} ^{\frac{\pi}{\mathrm{2}}} \frac{\mathrm{sin}\:^{\mathrm{3}} \mathrm{x}}{\mathrm{sin}\:^{\mathrm{3}} \mathrm{x}+\mathrm{cos}\:^{\mathrm{3}} ×}\mathrm{dx}=? \\ $$

Question Number 97091 Answers: 1 Comments: 0

solve ∫x^(x+1) dx .

$${solve}\:\int{x}^{{x}+\mathrm{1}} {dx}\:. \\ $$

Question Number 97089 Answers: 1 Comments: 0

solve ∫x^x (1+ln x)dx .

$${solve}\:\:\int{x}^{{x}} \left(\mathrm{1}+\mathrm{ln}\:{x}\right){dx}\:. \\ $$

Question Number 97082 Answers: 2 Comments: 0

Question Number 97059 Answers: 0 Comments: 1

Question Number 97057 Answers: 2 Comments: 0

∫_0 ^1 (dx/(√(−ln(x)))) ? [ by Gamma function ]

$$\underset{\mathrm{0}} {\overset{\mathrm{1}} {\int}}\:\frac{{dx}}{\sqrt{−\mathrm{ln}\left({x}\right)}}\:?\:\left[\:{by}\:{G}\mathrm{amma}\:\mathrm{function}\:\right] \\ $$

Question Number 97041 Answers: 2 Comments: 0

∫ sin^8 (x) cos^8 (x) dx = ?

$$\int\:\mathrm{sin}\:^{\mathrm{8}} \left({x}\right)\:\mathrm{cos}\:^{\mathrm{8}} \left({x}\right)\:{dx}\:=\:? \\ $$

Question Number 97007 Answers: 0 Comments: 16

Question Number 96990 Answers: 1 Comments: 0

∫_0 ^1 ((√x))^(√x) dx

$$\int_{\mathrm{0}} ^{\mathrm{1}} \left(\sqrt{\mathrm{x}}\right)^{\sqrt{\mathrm{x}}} \mathrm{dx} \\ $$

Question Number 96979 Answers: 1 Comments: 0

∫_0 ^π arctan(3^(cos(x)) )dx

$$\int_{\mathrm{0}} ^{\pi} {arctan}\left(\mathrm{3}^{{cos}\left({x}\right)} \right){dx} \\ $$

Question Number 96962 Answers: 1 Comments: 0

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

$$\mathrm{find}\:\:\int_{\mathrm{0}} ^{\mathrm{1}} \:\frac{\mathrm{dx}}{\sqrt{\mathrm{x}+\mathrm{1}}+\sqrt{\mathrm{2x}^{\mathrm{2}} +\mathrm{1}}} \\ $$

Question Number 96959 Answers: 1 Comments: 0

find ∫ arctan(x−(1/x))dx

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

Question Number 96958 Answers: 0 Comments: 0

let g(x) =ln(tanx) developp f at fourier serie

$$\mathrm{let}\:\mathrm{g}\left(\mathrm{x}\right)\:=\mathrm{ln}\left(\mathrm{tanx}\right) \\ $$$$\mathrm{developp}\:\mathrm{f}\:\mathrm{at}\:\mathrm{fourier}\:\mathrm{serie} \\ $$

Question Number 96957 Answers: 2 Comments: 0

find ∫ x^3 (√(2−x−x^2 ))dx

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

Question Number 96956 Answers: 2 Comments: 0

calculate ∫_(−∞) ^∞ ((x^2 −3)/((x^2 −x+1)^3 ))dx

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

Question Number 96955 Answers: 1 Comments: 0

let f(x) =ln(1+sinx) developp f at fourier serie

$$\mathrm{let}\:\mathrm{f}\left(\mathrm{x}\right)\:=\mathrm{ln}\left(\mathrm{1}+\mathrm{sinx}\right)\: \\ $$$$\mathrm{developp}\:\mathrm{f}\:\mathrm{at}\:\mathrm{fourier}\:\mathrm{serie} \\ $$

Question Number 96925 Answers: 2 Comments: 0

∫_0 ^1 ((ln(x^2 +1))/(x+1))dx

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

Question Number 96911 Answers: 1 Comments: 2

∫_(−∞) ^(+∞) ((x^2 sinh(x)+tan^(−1) (x)∙log(x^4 +1))/(πe^x^2 +((x^8 +3cosh(x)))^(1/3) ))dx

$$\int_{−\infty} ^{+\infty} \frac{\mathrm{x}^{\mathrm{2}} \mathrm{sinh}\left(\mathrm{x}\right)+\mathrm{tan}^{−\mathrm{1}} \left(\mathrm{x}\right)\centerdot\mathrm{log}\left(\mathrm{x}^{\mathrm{4}} +\mathrm{1}\right)}{\pi\mathrm{e}^{\mathrm{x}^{\mathrm{2}} } +\sqrt[{\mathrm{3}}]{\mathrm{x}^{\mathrm{8}} +\mathrm{3cosh}\left(\mathrm{x}\right)}}\mathrm{dx} \\ $$

Question Number 96898 Answers: 2 Comments: 1

Question Number 96886 Answers: 0 Comments: 3

solve by using trapezoidal rule h=0.2 and e=2.718 ∫_1 ^(2.2) (e^x^2 /x)dx

$${solve}\:{by}\:{using}\:{trapezoidal}\:{rule}\:{h}=\mathrm{0}.\mathrm{2} \\ $$$${and}\:{e}=\mathrm{2}.\mathrm{718} \\ $$$$\int_{\mathrm{1}} ^{\mathrm{2}.\mathrm{2}} \frac{{e}^{{x}^{\mathrm{2}} } }{{x}}{dx} \\ $$

Question Number 96883 Answers: 0 Comments: 2

solve by simpson′s rule ∫_1 ^(2.2) (e^x^2 /x)dx

$${solve}\:{by}\:{simpson}'{s}\:{rule}\: \\ $$$$\int_{\mathrm{1}} ^{\mathrm{2}.\mathrm{2}} \frac{{e}^{{x}^{\mathrm{2}} } }{{x}}{dx} \\ $$

Question Number 96864 Answers: 2 Comments: 1

∫ (dy/(y^2 (5−y^2 ))) ?

$$\int\:\frac{\mathrm{dy}}{\mathrm{y}^{\mathrm{2}} \left(\mathrm{5}−\mathrm{y}^{\mathrm{2}} \right)}\:? \\ $$

Question Number 96846 Answers: 0 Comments: 1

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