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IntegrationQuestion and Answers: Page 97

Question Number 133440 Answers: 1 Comments: 0

Question Number 133433 Answers: 2 Comments: 0

hi, everybody ! with I=∫_0 ^∞ (1/(x^4 +1)) dx, prove that : 2I=∫_0 ^∞ ((x^2 +1)/(x^4 +1)) dx.

$hi, everybody!$ $with I = \int_{0}^{\infty} \frac{1}{x^{4} + 1} d x,$ $prove that : 2 I = \int_{0}^{\infty} \frac{x^{2} + 1}{x^{4} + 1} d x .$

Question Number 133426 Answers: 1 Comments: 0

∫⌊x⌋dx=?...

$\int ⌊ x ⌋ d x = ? . . .$

Question Number 133369 Answers: 2 Comments: 2

calculus (2)..... 𝛗=∫_1 ^( 2) (((ln(((x+2)/(x+1))))/x))dx =???

$c a l c u l u s (2) . . . . .$ $ϕ = \int_{1}^{2} (\frac{l n (\frac{x + 2}{x + 1})}{x}) d x = ? ? ?$

Question Number 133872 Answers: 0 Comments: 3

∫(dx/((x^2 −1)(√(x^4 −1))))=?

$\int \frac{d x}{(x^{2} - 1) \sqrt{x^{4} - 1}} = ?$

Question Number 133360 Answers: 1 Comments: 2

∫ (√(1+sec x)) dx ?

$\int \sqrt{1 + \sec x} dx ?$

Question Number 133291 Answers: 1 Comments: 0

∫ (((x^4 )^2 )/((1+x^6 )^2 )) dx =?

$\int \frac{{(x^{4})}^{2}}{{(1 + x^{6})}^{2}} dx = ?$

Question Number 133305 Answers: 3 Comments: 0

∫_0 ^( 2π) (dx/(5+3sin 2x)) =?

$\int_{0}^{2 π} \frac{dx}{5 + 3 \sin 2 x} = ?$

Question Number 133222 Answers: 1 Comments: 0

∫_0 ^1 ((x^3 dx)/((x−1)^3 +3x−5))

$\underset{0}{\int^{1}} \frac{x^{3} dx}{{(x - 1)}^{3} + 3 x - 5}$

Question Number 133268 Answers: 1 Comments: 0

....calculus... prove:: 𝛗=∫_(−∞) ^( +∞) (dx/((x^2 +π^2 )cosh(x)))=(4/𝛑) −1

$. . . . c a l c u l u s . . .$ $p r o v e ::$ $ϕ = \int_{- \infty}^{+ \infty} \frac{d x}{(x^{2} + π^{2}) c o s h (x)} = \frac{4}{π} - 1$

Question Number 133214 Answers: 0 Comments: 0

calculate f(ξ) =∫_0 ^∞ ((x sin(ξx))/(1+x^4 ))dx

$calculate f (ξ) = \int_{0}^{\infty} \frac{x \sin (ξ x)}{1 + x^{4}} dx$

Question Number 133213 Answers: 1 Comments: 0

calculate c(ξ) =∫_0 ^∞ ((cos(ξx))/(1+x^4 ))dx

$calculate c (ξ) = \int_{0}^{\infty} \frac{\cos (ξ x)}{1 + x^{4}} dx$

Question Number 133228 Answers: 1 Comments: 0

....advanced calculus.... prove that :: Σ_(n=0) ^∞ ((Γ(n+(1/2))ψ(n+(1/2)))/(2^n .n!))=−(√(2π)) (γ+ln(2))....

$. . . . a d v a n c e d c a l c u l u s . . . .$ $p r o v e t h a t ::$ $\underset{n = 0}{\sum^{\infty}} \frac{Γ (n + \frac{1}{2}) ψ (n + \frac{1}{2})}{2^{n} . n!} = - \sqrt{2 π} (γ + l n (2)) . . . .$

Question Number 133187 Answers: 0 Comments: 0

.......CALCULUS...... lim _(n→∞) (n(ln(2)−Σ_(k=1) ^n (1/(n+k))))=?

$. . . . . . . C A L C U L U S . . . . . .$ $l i m_{n \to \infty} (n (l n (2) - \underset{k = 1}{\sum^{n}} \frac{1}{n + k})) = ?$

Question Number 133173 Answers: 3 Comments: 0

∫_0 ^( (1/2)) (√(1+(√(1−x^2 )))) dx =?

$\int_{0}^{\frac{1}{2}} \sqrt{1 + \sqrt{1 - x^{2}}} dx = ?$

Question Number 133125 Answers: 0 Comments: 1

find ∫_0 ^∞ ((cosx ch(2x))/((x^2 +x+3)^2 ))dx

$f i n d \int_{0}^{\infty} \frac{c o s x c h (2 x)}{{(x^{2} + x + 3)}^{2}} d x$

Question Number 133124 Answers: 0 Comments: 0

find ∫ (dx/((x+2)^2 (x^2 −x+1)^3 ))

$f i n d \int \frac{d x}{{(x + 2)}^{2} {(x^{2} - x + 1)}^{3}}$

Question Number 133123 Answers: 1 Comments: 0

find ∫ ((x^2 dx)/(x^3 −2x+1))

$f i n d \int \frac{x^{2} d x}{x^{3} - 2 x + 1}$

Question Number 133121 Answers: 1 Comments: 0

let u_n =Σ_(k=1) ^n (1/(√k)) find a equivalent of u_n (n+→∞)

$l e t u_{n} = \sum_{k = 1}^{n} \frac{1}{\sqrt{k}}$ $f i n d a e q u i v a l e n t o f u_{n} (n + \to \infty)$

Question Number 133120 Answers: 0 Comments: 0

calculate A_n = ∫∫_([(1/n),n[) (e^(−x^2 −y^2 ) /(√(x^2 +y^2 +3)))dxdy and lim_(n→∞) A_n

$c a l c u l a t e A_{n} = \int \int_{[\frac{1}{n}, n [} \frac{e^{- x^{2} - y^{2}}}{\sqrt{x^{2} + y^{2} + 3}} d x d y$ $a n d {l i m}_{n \to \infty} A_{n}$

Question Number 133119 Answers: 2 Comments: 0

find ∫_0 ^∞ ((xsin(2x))/((x^2 +4)^3 ))dx

$f i n d \int_{0}^{\infty} \frac{x s i n (2 x)}{{(x^{2} + 4)}^{3}} d x$

Question Number 133109 Answers: 2 Comments: 1

∫ (dx/((x^4 +1) ((x^4 +2))^(1/4) )) ?

$\int \frac{d x}{(x^{4} + 1) \sqrt[4]{x^{4} + 2}} ?$

Question Number 133107 Answers: 1 Comments: 0

... nice calculus... find:: 𝛗=^(???) ∫_0 ^( 1) (sin(x)+sin((1/x)))(dx/x)

$. . . n i c e c a l c u l u s . . .$ $f i n d :: ϕ \overset{? ? ?}{=} \int_{0}^{1} (s i n (x) + s i n (\frac{1}{x})) \frac{d x}{x}$

Question Number 133051 Answers: 0 Comments: 0

....advanced calculus.... evaluate: Σ_(n=1) ^∞ (H_n /(n^2 2^(n+1) ))=??

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

Question Number 133050 Answers: 2 Comments: 0

...nice ......calculus... 𝛗= ∫_(0 ) ^( 1) xli_3 (x)dx=???

$. . . n i c e . . . . . . c a l c u l u s . . .$ $ϕ = \int_{0}^{1} {x l i}_{3} (x) d x = ? ? ?$

Question Number 133048 Answers: 0 Comments: 0

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

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

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