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IntegrationQuestion and Answers: Page 104

Question Number 129907 Answers: 3 Comments: 0

∫(dx/(sin^3 xcos^5 x))=???????

$\int \frac{d x}{{s i n}^{3} {x c o s}^{5} x} = ? ? ? ? ? ? ?$

Question Number 129936 Answers: 2 Comments: 0

Nice integral ∫_0 ^( ∞) sin (x) ln (x) e^(−x) dx

$Nice integral$ $\int_{0}^{\infty} \sin (x) \ln (x) e^{- x} d x$

Question Number 129868 Answers: 1 Comments: 0

find lim_(n→+∞) (1/n)Σ_(k=0) ^(n−1) (k/( (√(4n^2 −k^2 ))))

$f i n d {l i m}_{n \to + \infty} \frac{1}{n} \sum_{k = 0}^{n - 1} \frac{k}{\sqrt{4 n^{2} - k^{2}}}$

Question Number 129867 Answers: 1 Comments: 0

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

$c a l c u l a t e \int \frac{2 x - 1}{{(x^{2} - x + 1)}^{3}} d x$

Question Number 129859 Answers: 3 Comments: 0

L = ∫_(−1) ^( 0) (√((1+y)/(1−y))) dy

$L = \int_{- 1}^{0} \sqrt{\frac{1 + y}{1 - y}} dy$

Question Number 129855 Answers: 2 Comments: 0

ϑ = ∫ (dx/((1+(√x) )^3 ))

$ϑ = \int \frac{d x}{{(1 + \sqrt{x})}^{3}}$

Question Number 129839 Answers: 7 Comments: 0

Question Number 129816 Answers: 1 Comments: 0

Question Number 129788 Answers: 1 Comments: 0

∫ (1+3x^3 )e^x^3 dx

$\int (1 + 3 x^{3}) e^{x^{3}} d x$

Question Number 129787 Answers: 1 Comments: 0

∫ x^7 (√(1+x^4 )) dx

$\int x^{7} \sqrt{1 + x^{4}} d x$

Question Number 129764 Answers: 2 Comments: 0

prove that ∫_(−∞) ^(+∞) x^2 e^(−x^2 ) cos(x^2 )sin(x^2 ) dx =(((√π)sin[(((√3)tan^(−1) (2))/2)])/(4 ((125))^(1/4) ))

$p r o v e t h a t$ $\int_{- \infty}^{+ \infty} x^{2} e^{- x^{2}} c o s (x^{2}) s i n (x^{2}) d x$ $= \frac{\sqrt{π} s i n [\frac{\sqrt{3} {t a n}^{- 1} (2)}{2}]}{4 \sqrt[4]{125}}$

Question Number 129746 Answers: 2 Comments: 0

N = ∫ ((3+2cos x)/(2+3cos x)) dx

$N = \int \frac{3 + 2 \cos x}{2 + 3 \cos x} dx$

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

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