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IntegrationQuestion and Answers: Page 3

Question Number 218583 Answers: 1 Comments: 0

∫_(0 ) ^∞ e^(−x) (Σ_(n=1) ^∞ ((f(n))/n) sin(nx))dx =1

$\int_{0}^{\infty} e^{- x} (\underset{n = 1}{\sum^{\infty}} \frac{f (n)}{n} s i n (n x)) d x = 1$

Question Number 218582 Answers: 1 Comments: 0

∫_0 ^∞ ((cos(ax) − cos(bx))/x^2 ) dx = (π/2) ∣b−a∣

$\int_{0}^{\infty} \frac{c o s (a x) - c o s (b x)}{x^{2}} d x = \frac{π}{2} ∣ b - a ∣$

Question Number 218563 Answers: 0 Comments: 0

solve for x ∈ R ∫_0 ^∞ ((sin(xt))/(e^t −1 )) dt = (𝛑/2) coth(𝛑x) − (1/(2x))

$s o l v e f o r x \in R$ $\int_{0}^{\infty} \frac{s i n (x t)}{e^{t} - 1} d t = \frac{π}{2} c o t h (π x) - \frac{1}{2 x}$

Question Number 218560 Answers: 0 Comments: 1

Question Number 218462 Answers: 2 Comments: 0

∫(dx/( (√(2x−x^2 +3))))

$\int \frac{d x}{\sqrt{2 x - x^{2} + 3}}$

Question Number 218398 Answers: 1 Comments: 0

Question Number 218395 Answers: 0 Comments: 0

Question Number 218383 Answers: 0 Comments: 2

Question Number 218376 Answers: 0 Comments: 0

∫_0 ^∞ ((J_𝛂 (ar))/((r^2 +k^2 )𝛍))dr

$\int_{0}^{\infty} \frac{J_{α} (a r)}{(r^{2} + k^{2}) μ} d r$

Question Number 218375 Answers: 1 Comments: 0

∫((√(tan x))/(sin^3 x cos x))dx

$\int \frac{\sqrt{t a n x}}{{s i n}^{3} x c o s x} d x$

Question Number 218374 Answers: 0 Comments: 0

∫_0 ^∞ J_α ((√(ar)))e^(−r) dr

$\int_{0}^{\infty} J_{α} (\sqrt{a r}) e^{- r} d r$

Question Number 218322 Answers: 1 Comments: 0

Evaluate ∫_0 ^(π/2) ((sin(x))/(sin^3 (x)+cos^3 (x))) dx.

$Evaluate \underset{0}{\int^{\frac{π}{2}}} \frac{\sin (x)}{\sin^{3} (x) + \cos^{3} (x)} d x .$

Question Number 218150 Answers: 1 Comments: 0

∫_0 ^1 (1/(1−x^2 ))ln(((1+x)/(2x)))dx

$\int_{0}^{1} \frac{1}{1 - x^{2}} l n (\frac{1 + x}{2 x}) d x$

Question Number 218148 Answers: 2 Comments: 0

I=∫_0 ^( ∞) ((sin((√( x ))))/( (( e^x ))^(1/4) ))dx=?

$I = \int_{0}^{\infty} \frac{\sin (\sqrt{x})}{\sqrt[4]{e^{x}}} d x = ?$

Question Number 218054 Answers: 0 Comments: 0

Question Number 217881 Answers: 2 Comments: 0

Question Number 217813 Answers: 1 Comments: 0

∫_0 ^∞ [(xp(2+x)]^(−1) dx p∈R

$\underset{0}{\int^{\infty}} [{(x p (2 + x)]}^{- 1} d x$ $p \in R$

Question Number 217804 Answers: 0 Comments: 0

Question Number 217755 Answers: 2 Comments: 2

∫ ((cos(sin^(− 1) x) + cos^(− 1) (sin x))/(ln(ln(ln(1 + (√(x + (√x)))))) dx

$\int \frac{\cos (\sin^{- 1} x) + \cos^{- 1} (\sin x)}{\ln (\ln (\ln (1 + \sqrt{x + \sqrt{x}})} dx$

Question Number 217761 Answers: 1 Comments: 0

prove that : I=∫_0 ^( ∞) ((sin(πx)sin(2πx)sin(3πx))/x^3 ) = π^3

$p r o v e t h a t :$ $I = \int_{0}^{\infty} \frac{s i n (π x) s i n (2 π x) s i n (3 π x)}{x^{3}} = π^{3}$

Question Number 217683 Answers: 0 Comments: 0

Prove:∫_0 ^1 (√((((√(K^2 +36K′^2 ))+6K^′ )/(K^2 +36K^(′2) )) ))(dk/( (√k)(1−k^2 )^(2/3) ))=(√π)((√2)−(√((4−2(√2))/3)))

$Prove : \int_{0}^{1} \sqrt{\frac{\sqrt{K^{2} + 36 K^{' 2}} + 6 K^{^{'}}}{K^{2} + 36 K^{^{'} 2}}} \frac{d k}{\sqrt{k} {(1 - k^{2})}^{\frac{2}{3}}} = \sqrt{π} (\sqrt{2} - \sqrt{\frac{4 - 2 \sqrt{2}}{3}})$

Question Number 217685 Answers: 0 Comments: 0

Question Number 217626 Answers: 1 Comments: 0

lim_( λ→0) ∫_λ ^( 2λ) (( e^(2t ) )/t) dt = ?

$\lim_{λ \to 0} \int_{λ}^{2 λ} \frac{e^{2 t}}{t} d t = ?$

Question Number 217441 Answers: 2 Comments: 0

∫_0 ^1 ((ln^3 (1−x))/x^3 ) dx=?

$\int_{0}^{1} \frac{\ln^{3} (1 - x)}{x^{3}} d x = ?$

Question Number 217431 Answers: 2 Comments: 0

Question Number 217423 Answers: 1 Comments: 0

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