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IntegrationQuestion and Answers: Page 163

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

Question Number 96834 Answers: 2 Comments: 1

1)calculate I_n = ∫_0 ^∞ (dx/((2x^2 +5x+3)^n )) 2) calculate ∫_0 ^∞ (dx/((2x^2 +5x+3)^2 )) and ∫_0 ^∞ (dx/((2x^2 +5x +3)^3 ))

$$\left.\mathrm{1}\right)\mathrm{calculate}\:\mathrm{I}_{\mathrm{n}} =\:\int_{\mathrm{0}} ^{\infty} \:\:\:\frac{\mathrm{dx}}{\left(\mathrm{2x}^{\mathrm{2}} +\mathrm{5x}+\mathrm{3}\right)^{\mathrm{n}} } \\ $$$$\left.\mathrm{2}\right)\:\mathrm{calculate}\:\int_{\mathrm{0}} ^{\infty} \:\frac{\mathrm{dx}}{\left(\mathrm{2x}^{\mathrm{2}} \:+\mathrm{5x}+\mathrm{3}\right)^{\mathrm{2}} }\:\mathrm{and}\:\int_{\mathrm{0}} ^{\infty} \:\frac{\mathrm{dx}}{\left(\mathrm{2x}^{\mathrm{2}} \:+\mathrm{5x}\:+\mathrm{3}\right)^{\mathrm{3}} } \\ $$

Question Number 96784 Answers: 1 Comments: 0

Question Number 96771 Answers: 1 Comments: 0

solve y^(′′) −y^′ +y = cos(2t) with y(0)=y^′ (0)=−1

$$\mathrm{solve}\:\mathrm{y}^{''} \:−\mathrm{y}^{'} \:+\mathrm{y}\:=\:\mathrm{cos}\left(\mathrm{2t}\right)\:\mathrm{with}\:\mathrm{y}\left(\mathrm{0}\right)=\mathrm{y}^{'} \left(\mathrm{0}\right)=−\mathrm{1} \\ $$

Question Number 96763 Answers: 2 Comments: 0

∫ ((sin ((x/2)) tan ((x/2)) dx)/(cos x)) = ?

$$\int\:\frac{\mathrm{sin}\:\left(\frac{\mathrm{x}}{\mathrm{2}}\right)\:\mathrm{tan}\:\left(\frac{\mathrm{x}}{\mathrm{2}}\right)\:\mathrm{dx}}{\mathrm{cos}\:\mathrm{x}}\:=\:? \\ $$

Question Number 96758 Answers: 0 Comments: 1

Let x∈ [ −((5π)/(12)) , −(π/3) ] . The maximum value of y = tan (x+((2π)/3))−tan (x+(π/6)) +cos (x+(π/6)) is ___

$$\mathrm{Let}\:{x}\in\:\left[\:−\frac{\mathrm{5}\pi}{\mathrm{12}}\:,\:−\frac{\pi}{\mathrm{3}}\:\right]\:.\:\mathrm{The}\:\mathrm{maximum}\: \\ $$$$\mathrm{value}\:\mathrm{of}\:\mathrm{y}\:=\:\mathrm{tan}\:\left({x}+\frac{\mathrm{2}\pi}{\mathrm{3}}\right)−\mathrm{tan}\:\left({x}+\frac{\pi}{\mathrm{6}}\right)\:+\mathrm{cos}\:\left({x}+\frac{\pi}{\mathrm{6}}\right) \\ $$$$\mathrm{is}\:\_\_\_ \\ $$

Question Number 96748 Answers: 0 Comments: 1

nobody tried question 94184...

$$\mathrm{nobody}\:\mathrm{tried}\:\mathrm{question}\:\mathrm{94184}... \\ $$

Question Number 96746 Answers: 3 Comments: 2

∫((√x)/((1+x^3 )(√(1−x^3 ))))dx=? ∫((√x)/((1−x^3 )(√(1+x^3 ))))dx=?

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

Question Number 96705 Answers: 1 Comments: 0

∫ ln((√(1−x))+(√(1+x))) dx = ?

$$\int\:\mathrm{ln}\left(\sqrt{\mathrm{1}−\mathrm{x}}+\sqrt{\mathrm{1}+\mathrm{x}}\right)\:\mathrm{dx}\:=\:? \\ $$

Question Number 96699 Answers: 0 Comments: 2

∫ ((tan^3 (ln x))/x) dx = ??

$$\int\:\frac{\mathrm{tan}^{\mathrm{3}} \left(\mathrm{ln}\:{x}\right)}{{x}}\:{dx}\:=\:?? \\ $$

Question Number 96693 Answers: 1 Comments: 0

Question Number 96679 Answers: 1 Comments: 0

I=∫_0 ^1 ((1−x)/(x^2 +(x^2 +1)^2 ))dx find tan(I)+sec(I)

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

Question Number 96672 Answers: 0 Comments: 1

Evaluate : ∫ ((log_x a)/x) dx

$${Evaluate}\:: \\ $$$$\int\:\frac{{log}_{{x}} {a}}{{x}}\:{dx} \\ $$

Question Number 96652 Answers: 1 Comments: 0

∫ ((xcos x−sin x)/(x^2 +sin^2 x)) dx

$$\int\:\frac{{x}\mathrm{cos}\:{x}−\mathrm{sin}\:{x}}{{x}^{\mathrm{2}} +\mathrm{sin}\:^{\mathrm{2}} {x}}\:{dx}\: \\ $$

Question Number 96637 Answers: 0 Comments: 1

Question Number 96613 Answers: 13 Comments: 0

∫secθdθ

$$\int\mathrm{sec}\theta\mathrm{d}\theta \\ $$

Question Number 96604 Answers: 0 Comments: 6

Please how will you evaluate ∫ (√dx) ???

$$\mathrm{Please}\:\mathrm{how}\:\mathrm{will}\:\mathrm{you}\:\mathrm{evaluate} \\ $$$$\:\int\:\sqrt{{dx}}\:??? \\ $$

Question Number 96595 Answers: 0 Comments: 0

∫_0 ^1 x^(4035) (x^4 +1)^(2017) (3x+1)^4 dx

$$\int_{\mathrm{0}} ^{\mathrm{1}} {x}^{\mathrm{4035}} \left({x}^{\mathrm{4}} +\mathrm{1}\right)^{\mathrm{2017}} \left(\mathrm{3}{x}+\mathrm{1}\right)^{\mathrm{4}} {dx} \\ $$

Question Number 96567 Answers: 1 Comments: 1

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