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∫e^(x^5 +8x^2 ) dx =((√π)/(4(√2)))e^x^5 erfi(2(√2)x)−((5(√π))/(4(128)(√2)))(super−erf_((hyper)) (2(√2)x))+c where[super−erf_((hyper)) (t)] is super−function in D_2 and [D_n ]

$$\int{e}^{{x}^{\mathrm{5}} +\mathrm{8}{x}^{\mathrm{2}} } {dx} \\ $$$$=\frac{\sqrt{\pi}}{\mathrm{4}\sqrt{\mathrm{2}}}{e}^{{x}^{\mathrm{5}} } {erfi}\left(\mathrm{2}\sqrt{\mathrm{2}}{x}\right)−\frac{\mathrm{5}\sqrt{\pi}}{\mathrm{4}\left(\mathrm{128}\right)\sqrt{\mathrm{2}}}\left({super}−{erf}_{\left({hyper}\right)} \left(\mathrm{2}\sqrt{\mathrm{2}}{x}\right)\right)+{c} \\ $$$$ \\ $$$${where}\left[{super}−{erf}_{\left({hyper}\right)} \left({t}\right)\right]\:{is}\:{super}−{function} \\ $$$${in}\:{D}_{\mathrm{2}} \:{and}\:\left[{D}_{{n}} \right] \\ $$

Question Number 98105 Answers: 2 Comments: 0

calculate ∫_3 ^(+∞) (((x+1)dx)/((x−2)^2 ( 2x+3)^3 ))

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

Question Number 98020 Answers: 1 Comments: 0

What is the area of the region bounded by x^2 +y^2 ≤ 9 ; x+y ≤ 3 and y ≤ x

$$\mathrm{What}\:\mathrm{is}\:\mathrm{the}\:\mathrm{area}\:\mathrm{of}\:\mathrm{the}\:\mathrm{region}\:\mathrm{bounded} \\ $$$$\mathrm{by}\:\mathrm{x}^{\mathrm{2}} +\mathrm{y}^{\mathrm{2}} \:\leqslant\:\mathrm{9}\:;\:\mathrm{x}+\mathrm{y}\:\leqslant\:\mathrm{3}\:\mathrm{and}\:\mathrm{y}\:\leqslant\:\mathrm{x}\: \\ $$

Question Number 98016 Answers: 1 Comments: 3

∫_0 ^1 ((ln^2 (x))/(x^2 +1)) dx ?

$$\underset{\mathrm{0}} {\overset{\mathrm{1}} {\int}}\:\frac{\mathrm{ln}^{\mathrm{2}} \left({x}\right)}{{x}^{\mathrm{2}} +\mathrm{1}}\:{dx}\:?\: \\ $$

Question Number 97928 Answers: 1 Comments: 0

find the general formula ∫_0 ^(π/2) tan^α (x) dx

$${find}\:{the}\:{general}\:{formula} \\ $$$$\int_{\mathrm{0}} ^{\frac{\pi}{\mathrm{2}}} {tan}^{\alpha} \left({x}\right)\:{dx} \\ $$

Question Number 97839 Answers: 3 Comments: 1

calculate A_n =∫_0 ^((nπ)/4) (dx/(3cos^4 x +3sin^4 x−1))

$$\mathrm{calculate}\:\mathrm{A}_{\mathrm{n}} =\int_{\mathrm{0}} ^{\frac{\mathrm{n}\pi}{\mathrm{4}}} \:\frac{\mathrm{dx}}{\mathrm{3cos}^{\mathrm{4}} \mathrm{x}\:+\mathrm{3sin}^{\mathrm{4}} \mathrm{x}−\mathrm{1}} \\ $$

Question Number 97800 Answers: 3 Comments: 0

1) findf(a)= ∫_0 ^1 (√(x^2 −x+a))dx with a>(1/2) 2)explicite g(a) =∫_0 ^1 (dx/(√(x^2 −x+a))) 3) calculate ∫_0 ^1 (dx/(√(x^2 −x +3)))

$$\left.\mathrm{1}\right)\:\mathrm{findf}\left(\mathrm{a}\right)=\:\int_{\mathrm{0}} ^{\mathrm{1}} \sqrt{\mathrm{x}^{\mathrm{2}} −\mathrm{x}+\mathrm{a}}\mathrm{dx}\:\:\:\:\:\mathrm{with}\:\mathrm{a}>\frac{\mathrm{1}}{\mathrm{2}} \\ $$$$\left.\mathrm{2}\right)\mathrm{explicite}\:\mathrm{g}\left(\mathrm{a}\right)\:=\int_{\mathrm{0}} ^{\mathrm{1}} \:\frac{\mathrm{dx}}{\sqrt{\mathrm{x}^{\mathrm{2}} −\mathrm{x}+\mathrm{a}}}\: \\ $$$$\left.\mathrm{3}\right)\:\mathrm{calculate}\:\int_{\mathrm{0}} ^{\mathrm{1}} \:\frac{\mathrm{dx}}{\sqrt{\mathrm{x}^{\mathrm{2}} −\mathrm{x}\:+\mathrm{3}}} \\ $$

Question Number 97794 Answers: 1 Comments: 3

solve y^(′′) +y =(1/(cosx))

$$\mathrm{solve}\:\mathrm{y}^{''} \:+\mathrm{y}\:=\frac{\mathrm{1}}{\mathrm{cosx}} \\ $$

Question Number 97782 Answers: 2 Comments: 1

Evaluate: ∫ ((sinx)/(1 +sin^2 x))dx

$${Evaluate}: \\ $$$$\int\:\frac{{sinx}}{\mathrm{1}\:+{sin}^{\mathrm{2}} {x}}{dx} \\ $$

Question Number 97759 Answers: 1 Comments: 0

∫ ((sin^5 (x) dx)/(√(cos (x)))) ?

$$\int\:\frac{\mathrm{sin}\:^{\mathrm{5}} \left({x}\right)\:{dx}}{\sqrt{\mathrm{cos}\:\left({x}\right)}}\:? \\ $$

Question Number 97721 Answers: 1 Comments: 3

Question Number 97892 Answers: 1 Comments: 0

Question Number 97707 Answers: 3 Comments: 0

Question Number 97683 Answers: 3 Comments: 3

Evaluate ∫_0 ^1 (1/(√(16 + 9x^2 ))) dx

$$\:\mathrm{Evaluate}\:\int_{\mathrm{0}} ^{\mathrm{1}} \frac{\mathrm{1}}{\sqrt{\mathrm{16}\:+\:\mathrm{9}{x}^{\mathrm{2}} }}\:{dx} \\ $$

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