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IntegrationQuestion and Answers: Page 126

Question Number 121859 Answers: 2 Comments: 0

find ∫ (dx/((x−1)(√(x+1))−(x+1)(√(x−1))))

$f i n d \int \frac{d x}{(x - 1) \sqrt{x + 1} - (x + 1) \sqrt{x - 1}}$

Question Number 121858 Answers: 0 Comments: 0

decompose F(x) =(x^n /(x^(2n+1) +1)) 2)find the value of ∫_0 ^∞ (x^n /(x^(2n+1) +1))dx n integr natural

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

Question Number 121857 Answers: 0 Comments: 0

find ∫_0 ^∞ xe^(−x^2 ) arctan(2x)dx

$f i n d \int_{0}^{\infty} {x e}^{- x^{2}} a r c t a n (2 x) d x$

Question Number 121908 Answers: 0 Comments: 0

Question Number 121854 Answers: 0 Comments: 0

Question Number 121825 Answers: 1 Comments: 1

∫ (dx/(x−4(√x))) ?

$\int \frac{d x}{x - 4 \sqrt{x}} ?$

Question Number 121814 Answers: 0 Comments: 0

Question Number 121774 Answers: 0 Comments: 0

... advanced calculus... evaluate: Σ_(n=1) ^∞ (((H_n )^2 )/n^2 ) =? where H_n =Σ_(k=1) ^n (1/k) (harmonic number)

$. . . a d v a n c e d c a l c u l u s . . .$ $e v a l u a t e :$ $\underset{n = 1}{\sum^{\infty}} \frac{{(H_{n})}^{2}}{n^{2}} = ?$ $w h e r e H_{n} = \underset{k = 1}{\sum^{n}} \frac{1}{k} (h a r m o n i c n u m b e r)$

Question Number 121766 Answers: 0 Comments: 0

The tangent line to y = f(x) at (3,4) is given y=3x−5. What is the tangent line to y = f^(−1) (x) at (3,4) where f(x) is an injective continous function that satisfies f(3)=4.

$The tangent line to y = f (x) at (3, 4) is$ $given y = 3 x - 5 . What is the tangent line$ $to y = f^{- 1} (x) at (3, 4) where f (x) is an$ $injective continous function that satisfies$ $f (3) = 4 .$

Question Number 121712 Answers: 1 Comments: 0

Question Number 121707 Answers: 1 Comments: 0

Question Number 121704 Answers: 1 Comments: 0

Question Number 121696 Answers: 2 Comments: 0

∫ ((x^4 −5x^3 +6x^2 −18)/(x^3 −3x^2 )) dx ?

$\int \frac{x^{4} - 5 x^{3} + 6 x^{2} - 18}{x^{3} - 3 x^{2}} d x ?$

Question Number 121680 Answers: 1 Comments: 0

please evaluate ∫x^x dx

$p l e a s e e v a l u a t e \int x^{x} d x$

Question Number 121674 Answers: 3 Comments: 0

... advanced calculus... prove that : Ω =∫_0 ^( ∞) ((sin^4 (x)ln(x))/x^2 )dx=(π/4)(1−γ) γ:euler−mascheroni constant m.n.july.1970

$. . . a d v a n c e d c a l c u l u s . . .$ $p r o v e t h a t :$ $Ω = \int_{0}^{\infty} \frac{{s i n}^{4} (x) l n (x)}{x^{2}} d x = \frac{π}{4} (1 - γ)$ $γ : e u l e r - m a s c h e r o n i c o n s t a n t$ $m . n . j u l y . 1970$

Question Number 121611 Answers: 1 Comments: 2

∫_0 ^2 sin (2πx)cos (5πx) dx ?

$\underset{0}{\int^{2}} \sin (2 π x) \cos (5 π x) dx ?$

Question Number 121602 Answers: 2 Comments: 0

Question Number 121601 Answers: 4 Comments: 0

∫ (dx/(x (√(3+x^2 )))) ?

$\int \frac{dx}{x \sqrt{3 + x^{2}}} ?$

Question Number 121548 Answers: 1 Comments: 0

∫_0 ^(π/4) tan^6 x sec x dx =?

$\underset{0}{\int^{π / 4}} \tan^{6} x \sec x dx = ?$

Question Number 121519 Answers: 1 Comments: 0

∫ ((1−x^4 )/(x^2 (√(x^4 +x^2 +1)))) dx ?

$\int \frac{1 - x^{4}}{x^{2} \sqrt{x^{4} + x^{2} + 1}} dx ?$

Question Number 121498 Answers: 1 Comments: 0

Evaluate Σ_(n=1) ^∞ ((sin(n))/n)

$Evaluate$ $\underset{n = 1}{\sum^{\infty}} \frac{\sin (n)}{n}$

Question Number 121500 Answers: 3 Comments: 1

(1) ∫ (dx/(x^4 +2x^2 +9)) ? (2) arc tan ((x/3))−arc tan ((x/3))= arc tan ((1/5))

$(1) \int \frac{dx}{x^{4} + {2 x}^{2} + 9} ?$ $(2) arc \tan (\frac{x}{3}) - arc \tan (\frac{x}{3}) = arc \tan (\frac{1}{5})$

Question Number 121492 Answers: 3 Comments: 0

calculate ∫_0 ^(+∞) (dx/((x^4 +1)^3 ))

$calculate \int_{0}^{+ \infty} \frac{dx}{{(x^{4} + 1)}^{3}}$

Question Number 121480 Answers: 0 Comments: 0

Question Number 121466 Answers: 1 Comments: 2

∫(√(cos(x) dx))

$\int \sqrt{c o s (x) d x}$

Question Number 121397 Answers: 2 Comments: 0

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