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IntegrationQuestion and Answers: Page 79

Question Number 141868 Answers: 1 Comments: 1

......Advanced .....Calculus........ ..... ∫_( R) ^ (e^(−x^2 ) /((1+x^2 )^2 )) dx=?

$. . . . . . A d v a n c e d . . . . . C a l c u l u s . . . . . . . .$ $. . . . . \int_{R}^{} \frac{e^{- x^{2}}}{{(1 + x^{2})}^{2}} d x = ?$

Question Number 141859 Answers: 2 Comments: 1

∫_0 ^∞ ((4e^(−x^2 ) )/((2x^2 +1)^2 )) dx

$\int_{0}^{\infty} \frac{4 e^{- x^{2}}}{{(2 x^{2} + 1)}^{2}} d x$

Question Number 141848 Answers: 4 Comments: 0

I = ∫ (1/( (√(1−x^2 ))−1)) dx

$I = \int \frac{1}{\sqrt{1 - x^{2}} - 1} d x$

Question Number 141847 Answers: 2 Comments: 0

I = ∫ ((sec x)/(1+csc x)) dx

$I = \int \frac{\sec x}{1 + \csc x} d x$

Question Number 142255 Answers: 1 Comments: 0

find the value of ∫_0 ^1 (√(x^4 −5x^2 +4)) dx? solution please.

$find the value of \int_{0}^{1} \sqrt{x^{4} - {5 x}^{2} + 4} dx ?$ $solution please .$

Question Number 142256 Answers: 1 Comments: 0

∫_0 ^∞ ((sinx)/x^(1−a) )dx

$\int_{0}^{\infty} \frac{s i n x}{x^{1 - a}} d x$

Question Number 141811 Answers: 1 Comments: 0

Θ:=(Σ_(n=1) ^∞ (n^4 /(2^n . n!)))^(1/2) =?

$Θ := {(\underset{n = 1}{\sum^{\infty}} \frac{n^{4}}{2^{n} . n!})}^{\frac{1}{2}} = ?$

Question Number 141757 Answers: 0 Comments: 1

Γ(n+(1/2))=(((√π)∙Γ(2n+1))/(2^(2n) Γ(n+1)))

$Γ (n + \frac{1}{2}) = \frac{\sqrt{π} \cdot Γ (2 n + 1)}{2^{2 n} Γ (n + 1)}$

Question Number 141755 Answers: 0 Comments: 0

Question Number 141719 Answers: 2 Comments: 0

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

$\int_{0}^{\infty} \frac{e^{- x^{2}}}{{(x^{2} + \frac{1}{2})}^{2}} d x = ?$

Question Number 141713 Answers: 1 Comments: 0

Question Number 141691 Answers: 1 Comments: 0

....Calculus(I).... 𝛗:=∫_(1/(2 )) ^( 1) (1/(x^2 (1+x^4 )^(3/4) ))dx=???

$. . . . C a l c u l u s (I) . . . .$ $ϕ := \int_{\frac{1}{2}}^{1} \frac{1}{x^{2} {(1 + x^{4})}^{\frac{3}{4}}} d x = ? ? ?$

Question Number 141685 Answers: 1 Comments: 0

......nice ... ... ... calculus..... If lim_(x→0) ((tan(x))/x) = 1 , prove that: lim(1/x)((1/x)−(1/(tan(x))))=(1/3)

$. . . . . . n i c e . . . . . . . . . c a l c u l u s . . . . .$ $I f {l i m}_{x \to 0} \frac{t a n (x)}{x} = 1, p r o v e t h a t :$ $l i m \frac{1}{x} (\frac{1}{x} - \frac{1}{t a n (x)}) = \frac{1}{3}$

Question Number 143167 Answers: 2 Comments: 0

∫arctan((√((√x)+1)))dx=??? propose′ par Rodrigue

$\int a r c t a n (\sqrt{\sqrt{x} + 1}) d x = ? ? ?$ ${p r o p o s e}^{'} p a r R o d r i g u e$

Question Number 141649 Answers: 1 Comments: 0

.......advanced calculus...... prove that−:: φ:=∫_0 ^( ∞) ((cos(2πx^2 ))/(cosh^2 (πx)))dx=(1/4) ✓

$. . . . . . . a d v a n c e d c a l c u l u s . . . . . .$ $p r o v e t h a t - ::$ $ϕ := \int_{0}^{\infty} \frac{c o s (2 π x^{2})}{{c o s h}^{2} (π x)} d x = \frac{1}{4} ✓$

Question Number 141623 Answers: 1 Comments: 0

Σ_(n=0) ^∞ (∫_0 ^1 (x^n /(1+x))dx)^2 =ln 2

$\underset{n = 0}{\sum^{\infty}} {(\int_{0}^{1} \frac{x^{n}}{1 + x} d x)}^{2} = l n 2$

Question Number 141599 Answers: 1 Comments: 1

∫_( 1) ^( 3) ∫_( − 1) ^( 1) ∫_( 0) ^( 2) (x + 2y − z) dx dy dz

$\int_{1}^{3} \int_{- 1}^{1} \int_{0}^{2} (x + 2 y - z) dx dy dz$

Question Number 141581 Answers: 1 Comments: 1

Σ_(n=0) ^∞ ∫_0 ^1 (x^n /(1+x))dx=?

$\underset{n = 0}{\sum^{\infty}} \int_{0}^{1} \frac{x^{n}}{1 + x} d x = ?$

Question Number 141577 Answers: 0 Comments: 0

((1/(1∙2∙3)))^2 +((1/(2∙3∙4)))^2 +((1/(3∙4∙5)))^2 +...=(1/(16))(4π^2 −39)

${(\frac{1}{1 \cdot 2 \cdot 3})}^{2} + {(\frac{1}{2 \cdot 3 \cdot 4})}^{2} + {(\frac{1}{3 \cdot 4 \cdot 5})}^{2} + . . . = \frac{1}{16} (4 π^{2} - 39)$

Question Number 141560 Answers: 1 Comments: 0

........Nice ....Calculus(I)...... Evaluate:: I:=∫_0 ^( ln(2)) (x/(e^x +2e^(−x) −2))dx=? ......

$. . . . . . . . N i c e . . . . C a l c u l u s (I) . . . . . .$ $E v a l u a t e ::$ $I := \int_{0}^{l n (2)} \frac{x}{e^{x} + 2 e^{- x} - 2} d x = ?$ $. . . . . .$

Question Number 141534 Answers: 1 Comments: 0

Question Number 141533 Answers: 1 Comments: 0

Question Number 141532 Answers: 1 Comments: 0

Question Number 141531 Answers: 0 Comments: 1

Question Number 141530 Answers: 0 Comments: 1

Question Number 141529 Answers: 0 Comments: 0

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