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IntegrationQuestion and Answers: Page 155

Question Number 100948 Answers: 0 Comments: 1

Question Number 100829 Answers: 0 Comments: 0

hello every one prove that ∫_0 ^(π/2) cos^u (x) cos(ax) arctan(b cos(x)) dx =((2^(−u−2) .π.b.Γ(u+2))/(Γ(((u−a+3)/2))Γ(((u+a+3)/2)))).x_4 F_3 ((((1/2),1+(u/2),((u+3)/2),−b^2 )),(((3/2),((u−a+3)/2),((u+a+3)/2))) ) Re u>−1 ,∣arg(1+b^2 ) ∣<π

$h e l l o e v e r y o n e$ $p r o v e t h a t$ $\int_{0}^{\frac{π}{2}} {c o s}^{u} (x) c o s (a x) a r c t a n (b c o s (x)) d x$ $= \frac{2^{- u - 2} . π . b . Γ (u + 2)}{Γ (\frac{u - a + 3}{2}) Γ (\frac{u + a + 3}{2})} . x_{4} F_{3} (\begin{matrix} \frac{1}{2}, 1 + \frac{u}{2}, \frac{u + 3}{2}, - b^{2} \\ \frac{3}{2}, \frac{u - a + 3}{2}, \frac{u + a + 3}{2} \end{matrix})$ $R e u > - 1, ∣ a r g (1 + b^{2}) ∣< π$

Question Number 100789 Answers: 2 Comments: 0

Question Number 100746 Answers: 1 Comments: 0

∫_(−∞) ^∞ ((cos3x)/((1+x^2 )^2 ))dx

$\int_{- \infty}^{\infty} \frac{c o s 3 x}{{(1 + x^{2})}^{2}} d x$

Question Number 100657 Answers: 1 Comments: 3

∫ ((3x−1)/(x^2 +9)) dx

$\int \frac{3 x - 1}{x^{2} + 9} d x$

Question Number 100653 Answers: 1 Comments: 0

Question Number 100613 Answers: 0 Comments: 0

Question Number 100606 Answers: 0 Comments: 0

∫e^(ix^(ix...∞) ) dx

$\int e^{{i x}^{i x . . . \infty}} d x$

Question Number 100590 Answers: 2 Comments: 0

∫_0 ^∞ (dx/((1+x^(18) )^2 ))

$\int_{0}^{\infty} \frac{d x}{{(1 + x^{18})}^{2}}$

Question Number 100584 Answers: 1 Comments: 0

∫i^i^(i......∞) dx

$\int i^{i^{i . . . . . . \infty}} d x$

Question Number 100557 Answers: 2 Comments: 0

Ω=∫_0 ^∞ (e^(ax) /(e^(bx) +1))dx, b>a

$Ω = \underset{0}{\int^{\infty}} \frac{e^{a x}}{e^{b x} + 1} d x, b > a$

Question Number 100538 Answers: 0 Comments: 1

Question Number 100543 Answers: 2 Comments: 1

Question Number 100514 Answers: 2 Comments: 0

calculatelim_(n→+∞) ∫_0 ^∞ (1−(x/n))^n ln(1+2x)dx

${calculatelim}_{n \to + \infty} \int_{0}^{\infty} {(1 - \frac{x}{n})}^{n} \ln (1 + 2 x) dx$

Question Number 100513 Answers: 0 Comments: 0

findA_(nm) =∫_0 ^∞ e^(−nx) ∣sin(px)∣ dx with n and p integr natural ≥1

${findA}_{nm} = \int_{0}^{\infty} e^{- nx} ∣ \sin (px) ∣ dx with n and p integr natural ⩾ 1$

Question Number 100512 Answers: 0 Comments: 0

calculate ∫_(−∞) ^(+∞) (x^n /((x^2 +x+1)^n )) dx with n integr and n≥2

$calculate \int_{- \infty}^{+ \infty} \frac{x^{n}}{{(x^{2} + x + 1)}^{n}} dx with n integr and n ⩾ 2$

Question Number 100511 Answers: 1 Comments: 0

calculate ∫_(−∞) ^∞ ((arctan(cosx +sinx))/(x^2 +4)) dx

$calculate \int_{- \infty}^{\infty} \frac{\arctan (cosx + sinx)}{x^{2} + 4} dx$

Question Number 100468 Answers: 3 Comments: 0

Σ_(n=1) ^∞ (n/((2n+1)!)) help me pls

$\underset{n = 1}{\sum^{\infty}} \frac{n}{(2 n + 1)!}$ $h e l p m e p l s$

Question Number 100450 Answers: 1 Comments: 0

Question Number 100438 Answers: 0 Comments: 5

∫_0 ^1 ∫_0 ^x x^2 y^(xy) dydx

$\int_{0}^{1} \int_{0}^{x} x^{2} y^{x y} d y d x$

Question Number 100362 Answers: 3 Comments: 0

∫_0 ^1 ∫_0 ^1 e^(2x+y) dydx

$\int_{0}^{1} \int_{0}^{1} e^{2 x + y} d y d x$

Question Number 100368 Answers: 1 Comments: 0

lim_(n→∞) ∫_(−∞) ^∞ cos (x^n ) dx =? where n=2k, k∈N, k≠0

$\lim_{n \to \infty} \int_{- \infty}^{\infty} \cos (x^{n}) d x = ?$ $w h e r e n = 2 k, k \in N, k \neq 0$

Question Number 100216 Answers: 1 Comments: 2

if I = ∫_0 ^(π/2) ((sin x)/(sin x + cos x))dx = ∫_0 ^(π/2) ((cos x)/(sin x +cos x))dx then I = ??

$if I = \int_{0}^{\frac{π}{2}} \frac{\sin x}{\sin x + \cos x} d x = \int_{0}^{\frac{π}{2}} \frac{\cos x}{\sin x + \cos x} d x$ $then I = ? ?$

Question Number 100215 Answers: 2 Comments: 1

evaluate lim_(n→∞) ∫_1 ^e x^n ln x dx

$evaluate \lim_{n \to \infty} \int_{1}^{e} x^{n} \ln x d x$

Question Number 100207 Answers: 0 Comments: 2

Given an even fuction f(x) such that ∫_(−a) ^a f(x)dx = (√a) ∀a ≥0 find ∫_3 ^4 f(x) dx

$Given an even fuction f (x) such that {\int^{a}}_{- a} f (x) d x = \sqrt{a} \forall a ⩾ 0$ $find \int_{3}^{4} f (x) d x$

Question Number 100191 Answers: 1 Comments: 1

∫ x^2 e^x dx ?

$\int x^{2} e^{x} d x ?$

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