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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 96922 Answers: 0 Comments: 8

Question Number 96920 Answers: 0 Comments: 2

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 96907 Answers: 0 Comments: 1

Σ_(z = 0) ^(10) cos^3 (((πz)/3)) = ?

$$\underset{\mathrm{z}\:=\:\mathrm{0}} {\overset{\mathrm{10}} {\sum}}\:\mathrm{cos}\:^{\mathrm{3}} \left(\frac{\pi\mathrm{z}}{\mathrm{3}}\right)\:=\:? \\ $$

Question Number 96906 Answers: 1 Comments: 0

Question Number 96904 Answers: 0 Comments: 3

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 96866 Answers: 1 Comments: 1

Question Number 96870 Answers: 2 Comments: 0

Question Number 96868 Answers: 0 Comments: 1

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 141856 Answers: 1 Comments: 0

Question Number 141855 Answers: 1 Comments: 0

Question Number 96848 Answers: 1 Comments: 0

Question Number 96846 Answers: 0 Comments: 1

Question Number 96845 Answers: 2 Comments: 0

If sin^(−1) (x/5) + cosec^(−1) (5/4) = (π/2), then x=

$$\mathrm{If}\:\mathrm{sin}^{−\mathrm{1}} \frac{{x}}{\mathrm{5}}\:+\:\mathrm{cosec}^{−\mathrm{1}} \frac{\mathrm{5}}{\mathrm{4}}\:=\:\frac{\pi}{\mathrm{2}},\:\mathrm{then}\:{x}= \\ $$

Question Number 96839 Answers: 0 Comments: 0

Question Number 96837 Answers: 1 Comments: 0

determine f continue on [a,b] wich verify (∫_a ^b f(x)dx)^2 =∫_a ^b f^2 (x)dx

$$\mathrm{determine}\:\mathrm{f}\:\mathrm{continue}\:\mathrm{on}\:\left[\mathrm{a},\mathrm{b}\right]\:\mathrm{wich}\:\mathrm{verify}\:\left(\int_{\mathrm{a}} ^{\mathrm{b}} \mathrm{f}\left(\mathrm{x}\right)\mathrm{dx}\right)^{\mathrm{2}} \:=\int_{\mathrm{a}} ^{\mathrm{b}} \:\mathrm{f}^{\mathrm{2}} \left(\mathrm{x}\right)\mathrm{dx} \\ $$

Question Number 96836 Answers: 2 Comments: 0

a_n is a sequence wich verify a_(n+1) +a_n =(1/(n+1)) ∀n calculate Σ_(n=0) ^∞ a_n x^n

$$\mathrm{a}_{\mathrm{n}} \:\mathrm{is}\:\mathrm{a}\:\mathrm{sequence}\:\mathrm{wich}\:\mathrm{verify}\:\mathrm{a}_{\mathrm{n}+\mathrm{1}} \:+\mathrm{a}_{\mathrm{n}} =\frac{\mathrm{1}}{\mathrm{n}+\mathrm{1}}\:\forall\mathrm{n} \\ $$$$\mathrm{calculate}\:\sum_{\mathrm{n}=\mathrm{0}} ^{\infty} \:\mathrm{a}_{\mathrm{n}} \mathrm{x}^{\mathrm{n}} \\ $$

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 96829 Answers: 0 Comments: 1

If 2f(x) + f(1−x) = x^2 . determine f(x)

$$\mathrm{If}\:\mathrm{2f}\left(\mathrm{x}\right)\:+\:\mathrm{f}\left(\mathrm{1}−\mathrm{x}\right)\:=\:\mathrm{x}^{\mathrm{2}} .\:\mathrm{determine}\:\mathrm{f}\left(\mathrm{x}\right) \\ $$

Question Number 96826 Answers: 1 Comments: 0

If 2f(x) + f(x−1) = x^2 . determine f(x)

$$\mathrm{If}\:\mathrm{2f}\left(\mathrm{x}\right)\:+\:\mathrm{f}\left(\mathrm{x}−\mathrm{1}\right)\:=\:\mathrm{x}^{\mathrm{2}} \:.\:\mathrm{determine}\:\mathrm{f}\left(\mathrm{x}\right)\: \\ $$

Question Number 96823 Answers: 2 Comments: 2

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