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let f(x) =∫_0 ^1 (dt/(ch(t)+xsh(t))) 1) find a explicit form of f(x) 2) determine g(x) =∫_0 ^1 (dt/((ch(t)+xsh(t))^2 )) 3) calculate ∫_0 ^1 (dt/(ch(t)+3sh(t))) and ∫_0 ^1 (dt/({ch(t)+3sh(t)}^2 ))

$l e t f (x) = \int_{0}^{1} \frac{d t}{c h (t) + x s h (t)}$ $1) f i n d a e x p l i c i t f o r m o f f (x)$ $2) d e t e r m i n e g (x) = \int_{0}^{1} \frac{d t}{{(c h (t) + x s h (t))}^{2}}$ $3) c a l c u l a t e \int_{0}^{1} \frac{d t}{c h (t) + 3 s h (t)} a n d \int_{0}^{1} \frac{d t}{{c h (t) + 3 s h (t)}^{2}}$

Question Number 66060 Answers: 0 Comments: 3

let f(x) =∫_0 ^(π/4) (dt/(x+tant)) with x real 1) find aexplicit form of f(x) 2)find also g(x) =∫_0 ^(π/4) (dt/((x+tant)^2 )) 3)give f^((n)) (x)at form of integral 4)calculate ∫_0 ^(π/4) (dt/(2+tant)) and ∫_0 ^(π/4) (dt/((2+tant)^2 ))

$l e t f (x) = \int_{0}^{\frac{π}{4}} \frac{d t}{x + t a n t} w i t h x r e a l$ $1) f i n d a e x p l i c i t f o r m o f f (x)$ $2) f i n d a l s o g (x) = \int_{0}^{\frac{π}{4}} \frac{d t}{{(x + t a n t)}^{2}}$ $3) g i v e f^{(n)} (x) a t f o r m o f i n t e g r a l$ $4) c a l c u l a t e \int_{0}^{\frac{π}{4}} \frac{d t}{2 + t a n t} a n d \int_{0}^{\frac{π}{4}} \frac{d t}{{(2 + t a n t)}^{2}}$

Question Number 66048 Answers: 0 Comments: 1

∫(x/(√(ln(1/x)))) dx

$\int \frac{x}{\sqrt{l n (1 / x)}} d x$

Question Number 66044 Answers: 1 Comments: 0

Question Number 65988 Answers: 3 Comments: 1

∫dx/x^2 −x+1

$\int d x / x^{2} - x + 1$

Question Number 66041 Answers: 0 Comments: 0

Question Number 65950 Answers: 4 Comments: 0

∫_0 ^( π/2) tan^3 xdx = ?

$\int_{0}^{π / 2} \tan^{3} x d x = ?$

Question Number 65945 Answers: 0 Comments: 2

pls i need solution plssss...asap n lim ∈ ((r^3 /(r^4 +n^4 ))) n→∞ r=1 please try and understand the way i typed it

$p l s i n e e d s o l u t i o n p l s s s s . . . a s a p$ $n$ $l i m \in (\frac{r^{3}}{r^{4} + n^{4}})$ $n \to \infty r = 1$ $p l e a s e t r y a n d u n d e r s t a n d t h e w a y i t y p e d i t$

Question Number 65926 Answers: 0 Comments: 0

find ∫_0 ^∞ e^(−x) ln(1+x^2 )dx

$f i n d \int_{0}^{\infty} e^{- x} l n (1 + x^{2}) d x$

Question Number 65925 Answers: 0 Comments: 3

calculate ∫_0 ^1 e^(−2t) ln(1−t)dt

$c a l c u l a t e \int_{0}^{1} e^{- 2 t} l n (1 - t) d t$

Question Number 65924 Answers: 0 Comments: 1

calculate ∫_(−(π/6)) ^(π/6) (x/(sinx))dx

$c a l c u l a t e \int_{- \frac{π}{6}}^{\frac{π}{6}} \frac{x}{s i n x} d x$

Question Number 65923 Answers: 0 Comments: 0

calculate ∫_0 ^∞ ((1−cos(2x^2 ))/x^2 )dx

$c a l c u l a t e \int_{0}^{\infty} \frac{1 - c o s (2 x^{2})}{x^{2}} d x$

Question Number 65922 Answers: 0 Comments: 1

calculate ∫_0 ^∞ ((sin(3x^2 ))/x^2 )dx

$c a l c u l a t e \int_{0}^{\infty} \frac{s i n (3 x^{2})}{x^{2}} d x$

Question Number 65920 Answers: 1 Comments: 1

fnd ∫ (dx/(x+2−(√(3+x^2 ))))

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

Question Number 65919 Answers: 1 Comments: 1

find ∫ (dx/(x(√(x+1)) +(x+1)(√x))) 2) calculate ∫_1 ^(√3) (dx/(x(√(x+1)) +(x+1)(√x)))

$f i n d \int \frac{d x}{x \sqrt{x + 1} + (x + 1) \sqrt{x}}$ $2) c a l c u l a t e \int_{1}^{\sqrt{3}} \frac{d x}{x \sqrt{x + 1} + (x + 1) \sqrt{x}}$

Question Number 65878 Answers: 0 Comments: 5

Calculate lim_(a−>∞) ∫_0 ^∞ (dx/(1+x^a ))

$C a l c u l a t e {l i m}_{a - > \infty} \int_{0}^{\infty} \frac{d x}{1 + x^{a}}$

Question Number 65837 Answers: 0 Comments: 4

1) calculate ∫_(−∞) ^∞ (dx/(1+ix)) and ∫_(−∞) ^∞ (dx/(1−ix)) 2)deduce the value of ∫_(−∞) ^∞ (dx/(1+x^2 )) 3)calculate ∫_(−∞) ^∞ (dx/(1+ix^2 )) and ∫_(−∞) ^∞ (dx/(1−ix^2 )) 4)deduce the value of ∫_(−∞) ^∞ (dx/(1+x^4 ))

$1) c a l c u l a t e \int_{- \infty}^{\infty} \frac{d x}{1 + i x} a n d \int_{- \infty}^{\infty} \frac{d x}{1 - i x}$ $2) d e d u c e t h e v a l u e o f \int_{- \infty}^{\infty} \frac{d x}{1 + x^{2}}$ $3) c a l c u l a t e \int_{- \infty}^{\infty} \frac{d x}{1 + {i x}^{2}} a n d \int_{- \infty}^{\infty} \frac{d x}{1 - {i x}^{2}}$ $4) d e d u c e t h e v a l u e o f \int_{- \infty}^{\infty} \frac{d x}{1 + x^{4}}$

Question Number 65834 Answers: 0 Comments: 1

∀ x, y >0 B(x,y)=∫_0 ^1 t^(x−1) (1−t)^(y−1) dt Γ(x)=∫_0 ^∞ t^(x−1) e^(−t) dt 1) show that ∀ x>0 Γ(x+1)=xΓ(x) and lim_(n−>∞) ((x(x+1)......(x+n))/(n^x n!))=(1/(Γ(x))) and deduce that lim_(n−>∞) ((Γ(x+n))/(n^x Γ(n)))=1 b) Prove that if a function f satisfies f(x+1)=xf(x) et lim_(n−>∞) ((f(x+n))/(n^x f(n)))=1 then ∀ x>0 f(x)= f(1)Γ(x) 3) Show that B(x+1, y)=(x/(x+y))B(x,y) B(1,x)=(1/x) 2) Now let consider ∀ y f(x)=((B(x,y)Γ(x+y))/(Γ(y))) Show that f verify the same property as Γ ( just the both proved up ) 3) Deduce that ∀ x,y>0 B(x,y)=((Γ(x)Γ(y))/(Γ(x+y)))

$\forall x, y > 0 B (x, y) = \int_{0}^{1} t^{x - 1} {(1 - t)}^{y - 1} d t Γ (x) = \int_{0}^{\infty} t^{x - 1} e^{- t} d t$ $1) s h o w t h a t \forall x > 0 Γ (x + 1) = x Γ (x) a n d {l i m}_{n - > \infty} \frac{x (x + 1) . . . . . . (x + n)}{n^{x} n!} = \frac{1}{Γ (x)}$ $a n d d e d u c e t h a t {l i m}_{n - > \infty} \frac{Γ (x + n)}{n^{x} Γ (n)} = 1$ $b) P r o v e t h a t i f a f u n c t i o n f s a t i s f i e s f (x + 1) = x f (x) e t {l i m}_{n - > \infty} \frac{f (x + n)}{n^{x} f (n)} = 1 t h e n \forall x > 0 f (x) = f (1) Γ (x)$ $3) S h o w t h a t B (x + 1, y) = \frac{x}{x + y} B (x, y) B (1, x) = \frac{1}{x}$ $2) N o w l e t c o n s i d e r \forall y f (x) = \frac{B (x, y) Γ (x + y)}{Γ (y)}$ $S h o w t h a t f v e r i f y t h e s a m e p r o p e r t y a s Γ (j u s t t h e b o t h p r o v e d u p)$ $3) D e d u c e t h a t \forall x, y > 0 B (x, y) = \frac{Γ (x) Γ (y)}{Γ (x + y)}$

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