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IntegrationQuestion and Answers: Page 106

Question Number 129763 Answers: 2 Comments: 0

prove ∫_(−∞) ^(+∞) (1/(1+e^x^2 ))dx=(√π) (1−(√2) )ξ((1/2))

$p r o v e$ $\int_{- \infty}^{+ \infty} \frac{1}{1 + e^{x^{2}}} d x = \sqrt{π} (1 - \sqrt{2}) ξ (\frac{1}{2})$

Question Number 129696 Answers: 1 Comments: 5

nice old question by sir m?th+et?s ∫_0 ^∞ cos((x^3 /3)+tx)dx

$n i c e o l d q u e s t i o n b y s i r m ? t h + e t ? s$ $\int_{0}^{\infty} c o s (\frac{x^{3}}{3} + t x) d x$

Question Number 129794 Answers: 3 Comments: 0

∫ (x^2 −1)(x+1)^(−2/3) dx ?

$\int (x^{2} - 1) {(x + 1)}^{- 2 / 3} dx ?$

Question Number 129688 Answers: 1 Comments: 0

complex analysis ∮_C ((ϱ^(2z) +sinz^2 )/((z−2)(z−3)))dz C:∣Z∣=5

$c o m p l e x a n a l y s i s$ $\oint_{C} \frac{ϱ^{2 z} + {s i n z}^{2}}{(z - 2) (z - 3)} d z C :∣ Z ∣= 5$

Question Number 129684 Answers: 3 Comments: 0

... advanced calculus... prove that: ∫_0 ^( π) cos(tan(x)−cot(x))dx=(π/e^2 )

$. . . a d v a n c e d c a l c u l u s . . .$ $p r o v e t h a t :$ $\int_{0}^{π} c o s (t a n (x) - c o t (x)) d x = \frac{π}{e^{2}}$

Question Number 129651 Answers: 0 Comments: 0

... nice calculus... evaluate :: Σ_(n=1) ^∞ (((−1)^n )/(n^2 +1)) (((sin(n))/n))^2 =?

$. . . n i c e c a l c u l u s . . .$ $e v a l u a t e ::$ $\underset{n = 1}{\sum^{\infty}} \frac{{(- 1)}^{n}}{n^{2} + 1} {(\frac{s i n (n)}{n})}^{2} = ?$

Question Number 129645 Answers: 1 Comments: 0

ϝ = ∫ (dx/(1+x^(12) )) .

$ϝ = \int \frac{d x}{1 + x^{12}} .$

Question Number 129646 Answers: 3 Comments: 0

ϝ = ∫ (dx/(x^(2n+1) (x^n −1)))

$ϝ = \int \frac{d x}{x^{2 n + 1} (x^{n} - 1)}$

Question Number 129635 Answers: 3 Comments: 1

∫(dx/((x^2 +1)^2 ))=? Σ_(k=1) ^n (1/(k(k+1)(2k+1)))=?

$\int \frac{d x}{{(x^{2} + 1)}^{2}} = ?$ $\underset{k = 1}{\sum^{n}} \frac{1}{k (k + 1) (2 k + 1)} = ?$

Question Number 129576 Answers: 1 Comments: 0

please, how to show that f : [0 , a] × R_+ → R (x, y) e^(−xy) sin x is integrable ???

$please, how to show that$ $f : [0, a] \times R_{+} \to R$ $(x, y) e^{- x y} s i n x$ $is integrable ? ? ?$

Question Number 129564 Answers: 2 Comments: 0

V = ∫ ((sin x)/(sin (x+θ))) dx

$V = \int \frac{\sin x}{\sin (x + θ)} dx$

Question Number 129562 Answers: 1 Comments: 0

calculate ∫_0 ^∞ (dx/((x^6 +1)^2 ))

$calculate \int_{0}^{\infty} \frac{dx}{{(x^{6} + 1)}^{2}}$

Question Number 129558 Answers: 1 Comments: 0

...modern ∗∗∗∗∗∗∗∗∗∗ algebra ... ::: if ′′ G ′′ be a finite group and O (G)=pq , where ′′ p , q ′′ are two prime numbers (p > q ) then prove that: G has at most one subgroup of order ′′ p ′′ . written and compiled by ...♣m.n.july.1970♣....

$. . . m o d e r n * * * * * * * * * * a l g e b r a . . .$ $::: i f^{″} G^{″} b e a f i n i t e g r o u p a n d$ $O (G) = p q, w h e r e^{″} p, q^{″} a r e t w o$ $p r i m e n u m b e r s (p > q) t h e n p r o v e t h a t :$ $G h a s a t m o s t o n e s u b g r o u p o f o r d e r^{″} p^{″} .$ $w r i t t e n a n d c o m p i l e d b y$ $. . . ♣ m . n . j u l y . 1970 ♣ . . . .$

Question Number 129594 Answers: 0 Comments: 1

Question Number 129519 Answers: 1 Comments: 0

∫ cos (y^3 )dy

$\int c o s (y^{3}) d y$

Question Number 129503 Answers: 0 Comments: 2

Question Number 129418 Answers: 3 Comments: 0

...advsnced calculus.... calculate: Ω=∫_0 ^( ∞) e^(−(√x) ) ln(1+(1/( (√x) )))dx

$. . . a d v s n c e d c a l c u l u s . . . .$ $c a l c u l a t e : Ω = \int_{0}^{\infty} e^{- \sqrt{x}} l n (1 + \frac{1}{\sqrt{x}}) d x$

Question Number 129377 Answers: 2 Comments: 0

∫(( (√x))/( (√(x-1))))dx = ...

$\int \frac{\sqrt{x}}{\sqrt{x - 1}} dx = . . .$

Question Number 129370 Answers: 1 Comments: 0

Question Number 129318 Answers: 1 Comments: 0

... laplace transformation.. L (te^(−t) ⌊t⌋)=? note : ⌊x⌋ is floor of ′′ x ′′... ..............

$. . . l a p l a c e t r a n s f o r m a t i o n . .$ $L ({t e}^{- t} ⌊ t ⌋) = ?$ $n o t e : ⌊ x ⌋ i s f l o o r o f^{″} x^{″} . . .$ $. . . . . . . . . . . . . .$

Question Number 129277 Answers: 0 Comments: 0

O = ∫_( 0) ^( 1) ((arctan (((3X+3)/(1−2X−X^2 ))))/(1+X^2 )) dX

$O = \int_{0}^{1} \frac{\arctan (\frac{3 X + 3}{1 - 2 X - X^{2}})}{1 + X^{2}} dX$

Question Number 129275 Answers: 0 Comments: 2

∫e^x^x dx??????

$\int e^{x^{x}} dx ? ? ? ? ? ?$

Question Number 129274 Answers: 1 Comments: 0

∫ ((cos^2 x+cos x)/(1+sin x+cos x)) dx ?

$\int \frac{\cos^{2} x + \cos x}{1 + \sin x + \cos x} dx ?$

Question Number 129273 Answers: 0 Comments: 0

please answer my question

$please answer my question$

Question Number 129269 Answers: 1 Comments: 0

∫_1 ^a ((4(√x) +k)/( (√x) +1)) = 4a+3 . Find the value of ∫_1 ^( a) (1/( (√x) +1)) dx .

$\int_{1}^{a} \frac{4 \sqrt{x} + k}{\sqrt{x} + 1} = 4 a + 3 . Find the value$ $of \int_{1}^{a} \frac{1}{\sqrt{x} + 1} d x .$

Question Number 129251 Answers: 3 Comments: 1

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