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Question Number 131974 Answers: 2 Comments: 0

Question Number 131969 Answers: 1 Comments: 0

... math analysis... φ= ∫_(−∞) ^( +∞) ((xsin(x))/(x^2 +2x+2))dx=? φ=∫_(−∞) ^( +∞) ((xsin(x))/((x+1)^2 +1))dx =^(x+1=t) ∫_(−∞) ^( +∞) (((t−1)sin(t−1))/(t^2 +1))dt =∫_(−∞) ^( +∞) ((tsin(t)cos(1)−tcos(t)sin(1)−sin(t)cos(1)+cos(t)sin(1))/(t^2 +1))dt =2cos(1)∫_0 ^( ∞) ((tsin(t))/(t^2 +1))dt+2sin(1)∫_0 ^( ∞) ((cos(t))/(t^2 +1))dt =2cos(1).(π/(2e))+2sin(1).(π/(2e)) =(π/e)(cos(1)+sin(1))....

$. . . m a t h a n a l y s i s . . .$ $ϕ = \int_{- \infty}^{+ \infty} \frac{x s i n (x)}{x^{2} + 2 x + 2} d x = ?$ $ϕ = \int_{- \infty}^{+ \infty} \frac{x s i n (x)}{{(x + 1)}^{2} + 1} d x$ $\overset{x + 1 = t}{=} \int_{- \infty}^{+ \infty} \frac{(t - 1) s i n (t - 1)}{t^{2} + 1} d t$ $= \int_{- \infty}^{+ \infty} \frac{t s i n (t) c o s (1) - t c o s (t) s i n (1) - s i n (t) c o s (1) + c o s (t) s i n (1)}{t^{2} + 1} d t$ $= 2 c o s (1) \int_{0}^{\infty} \frac{t s i n (t)}{t^{2} + 1} d t + 2 s i n (1) \int_{0}^{\infty} \frac{c o s (t)}{t^{2} + 1} d t$ $= 2 c o s (1) . \frac{π}{2 e} + 2 s i n (1) . \frac{π}{2 e}$ $= \frac{π}{e} (c o s (1) + s i n (1)) . . . .$

Question Number 131961 Answers: 2 Comments: 0

∫(sin^4 x.cos^4 x)dx

$\int ({s i n}^{4} x . {c o s}^{4} x) d x$

Question Number 131957 Answers: 2 Comments: 0

Evaluate ∫_(−∞) ^∞ ((sinx)/(x^2 +2x+2))dx

$E v a l u a t e \int_{- \infty}^{\infty} \frac{s i n x}{x^{2} + 2 x + 2} d x$

Question Number 131919 Answers: 1 Comments: 0

Question Number 131891 Answers: 0 Comments: 0

∫ ((x!)/( (√x))) dx = ?

$\int \frac{x!}{\sqrt{x}} d x = ?$

Question Number 131875 Answers: 1 Comments: 0

...nice calculus.. Φ=∫_0 ^( ∞) ((ln(cosh(x)))/(cosh(x)))dx=???

$. . . n i c e c a l c u l u s . .$ $Φ = \int_{0}^{\infty} \frac{l n (c o s h (x))}{c o s h (x)} d x = ? ? ?$

Question Number 131874 Answers: 0 Comments: 0

... calculus ... φ =∫_0 ^( ∞) ((tanh^2 (x)dx)/x^2 ) =?

$. . . c a l c u l u s . . .$ $ϕ = \int_{0}^{\infty} \frac{{t a n h}^{2} (x) d x}{x^{2}} = ?$

Question Number 131866 Answers: 2 Comments: 0

...advanced calculus... Ω=∫_0 ^( ∞) (dx/(x^5 (e^(1/x) −1)))=?

$. . . a d v a n c e d c a l c u l u s . . .$ $Ω = \int_{0}^{\infty} \frac{d x}{x^{5} (e^{\frac{1}{x}} - 1)} = ?$

Question Number 131852 Answers: 1 Comments: 0

... analysis (II)... evaluate :: ∅=∫_1 ^( 10) x^2 d({x})=? {x} :: fractional part of x ...

$. . . a n a l y s i s (I I) . . .$ $e v a l u a t e ::$ $\emptyset = \int_{1}^{10} x^{2} d ({x}) = ?$ ${x} :: f r a c t i o n a l p a r t o f x . . .$

Question Number 131849 Answers: 3 Comments: 0

∗∗∗ calculus (I) ∗∗∗ please evaluate:: φ=∫(dx/(sin(2x)ln(tan(x)))) Trinity College Cambridge ....1897...

$* * * c a l c u l u s (I) * * *$ $p l e a s e e v a l u a t e ::$ $ϕ = \int \frac{d x}{s i n (2 x) l n (t a n (x))}$ $T r i n i t y C o l l e g e$ $C a m b r i d g e . . . . 1897 . . .$

Question Number 131816 Answers: 0 Comments: 0

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

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

Question Number 131810 Answers: 1 Comments: 0

f(x)= { ((−2x ; x≤0)),((f(x−1) ; x>0)) :} ∫_0 ^(100) f(x)dx =?

$f (x) = {\begin{cases} - 2 x; x ⩽ 0 \\ f (x - 1); x > 0 \end{cases}$ $\underset{0}{\int^{100}} f (x) d x = ?$

Question Number 131807 Answers: 1 Comments: 1

f(x)=2−x ∫_0 ^1 f(x)dx ⇒ ∫_0 ^1 f(x)dx=?

$f (x) = 2 - x \underset{0}{\int^{1}} f (x) d x \Rightarrow \underset{0}{\int^{1}} f (x) d x = ?$

Question Number 131743 Answers: 1 Comments: 0

∫_(C:∣z∣=1) ((−2i)/(Az^2 +2z+A))dz where C is a unit circle with radius 1

$\int_{C :∣ z ∣= 1} \frac{- 2 i}{{A z}^{2} + 2 z + A} d z w h e r e C i s a u n i t c i r c l e w i t h r a d i u s 1$

Question Number 131711 Answers: 0 Comments: 1

advanced cslculus .. prove that: Σ_(n=0 ) ^∞ (1/(16^n ))((4/(8n+1))−(2/(8n+4))−(1/(8n+5))−(1/(8n+6)))=π

$a d v a n c e d c s l c u l u s . .$ $p r o v e t h a t :$ $\underset{n = 0}{\sum^{\infty}} \frac{1}{16^{n}} (\frac{4}{8 n + 1} - \frac{2}{8 n + 4} - \frac{1}{8 n + 5} - \frac{1}{8 n + 6}) = π$

Question Number 131689 Answers: 0 Comments: 0

a curve C passes through (2,0) and the slope at (x,y) as (((x+1)^2 +(y−3))/(x+1)) Find the equation of the curve.

$a curve C passes through (2, 0)$ $and the slope at (x, y) as \frac{{(x + 1)}^{2} + (y - 3)}{x + 1}$ $Find the equation of the curve .$

Question Number 131678 Answers: 2 Comments: 0

Nice calculus ∫_0 ^∞ ((x^(n−2) −1)/(x^n +1)) dx ?

$Nice calculus$ $\int_{0}^{\infty} \frac{x^{n - 2} - 1}{x^{n} + 1} dx ?$

Question Number 131674 Answers: 0 Comments: 0

Given y=f(x) satisfies (dy/dx) + ((√((x^2 −1)(y^2 −1)))/(xy)) = 1 lies at point (1,1) and ((√2) ,k). find k .

$Given y = f (x) satisfies$ $\frac{dy}{dx} + \frac{\sqrt{(x^{2} - 1) (y^{2} - 1)}}{xy} = 1$ $lies at point (1, 1) and (\sqrt{2}, k) .$ $find k .$

Question Number 131673 Answers: 4 Comments: 0

Nice integral ∫_0 ^( 1) ((sin (ln x))/(ln x)) dx =?

$Nice integral$ $\int_{0}^{1} \frac{\sin (\ln x)}{\ln x} dx = ?$

Question Number 131637 Answers: 2 Comments: 0

Question Number 131630 Answers: 0 Comments: 0

Question Number 131614 Answers: 0 Comments: 0

...nice calculus... prove that : ∫_0 ^( 1) ln(Γ(x))cos(2πnx)dx=(1/(4n)) for example :∫_0 ^( 1) ln(Γ(x))cos(2πx)dx=(1/4)

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

Question Number 131602 Answers: 2 Comments: 0

Question Number 131581 Answers: 0 Comments: 1

... nice calculus... evaluate :: Ω=∫_0 ^( ∞) ((sin(x))/x)ln(((a+cos^2 (x))/(b+cos^2 (x))))dx=?

$. . . n i c e c a l c u l u s . . .$ $e v a l u a t e ::$ $Ω = \int_{0}^{\infty} \frac{s i n (x)}{x} l n (\frac{a + {c o s}^{2} (x)}{b + {c o s}^{2} (x)}) d x = ?$

Question Number 131558 Answers: 1 Comments: 0

∫_0 ^1 (dx/( (√(1−x^4 )))) =?

$\int_{0}^{1} \frac{dx}{\sqrt{1 - x^{4}}} = ?$

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