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IntegrationQuestion and Answers: Page 133

Question Number 116318 Answers: 1 Comments: 0

1) explicite f(a) =∫_(−∞) ^(+∞) ((arctan(a+x))/(x^2 +4))dx 1) 1)calculate ∫_(−∞) ^(+∞) ((arctan(1+x))/(x^2 +4))dx and ∫_(−∞) ^(+∞) ((arctan(3+x))/(x^2 +4))dx

$1) e x p l i c i t e f (a) = \int_{- \infty}^{+ \infty} \frac{a r c t a n (a + x)}{x^{2} + 4} d x$ $1) 1) c a l c u l a t e \int_{- \infty}^{+ \infty} \frac{a r c t a n (1 + x)}{x^{2} + 4} d x$ $a n d \int_{- \infty}^{+ \infty} \frac{a r c t a n (3 + x)}{x^{2} + 4} d x$

Question Number 116311 Answers: 3 Comments: 0

∫_0 ^(π/3) ((sin 2x)/((sin x)^(4/3) )) dx

$\underset{0}{\int^{\frac{π}{3}}} \frac{\sin 2 x}{{(\sin x)}^{\frac{4}{3}}} dx$

Question Number 116299 Answers: 0 Comments: 0

... advanced math ... evaluate that : Ω=∫_0 ^( 1) [(1/(ln(x))) +(1/(1−x)) ]^2 dx=??? m.n

$. . . a d v a n c e d m a t h . . .$ $e v a l u a t e t h a t :$ $Ω = \int_{0}^{1} {[\frac{1}{l n (x)} + \frac{1}{1 - x}]}^{2} d x = ? ? ?$ $m . n$

Question Number 116272 Answers: 1 Comments: 0

∫_0 ^(π/2) ln(x^2 +ln^2 (cos(x)))dx=πln(ln(2)) posted Quation not solved yet i hop someon Giv idea for this one thank you

$\int_{0}^{\frac{π}{2}} l n (x^{2} + {l n}^{2} (c o s (x))) d x = π l n (l n (2))$ $p o s t e d Q u a t i o n$ $n o t s o l v e d y e t i h o p s o m e o n G i v i d e a f o r$ $t h i s o n e t h a n k y o u$

Question Number 116250 Answers: 0 Comments: 0

1)explicite U_n =∫_0 ^∞ e^(−n[x]) cos(3[x])dx 2) calculate lim_(n→+∞) U_n 3)find nsture of Σ U_n

$1) explicite U_{n} = \int_{0}^{\infty} e^{- n [x]} \cos (3 [x]) dx$ $2) calculate \lim_{n \to + \infty} U_{n}$ $3) find nsture of Σ U_{n}$

Question Number 116249 Answers: 0 Comments: 0

find ∫_0 ^1 ((arctan(x^2 +3))/(x^2 +3))dx

$find \int_{0}^{1} \frac{\arctan (x^{2} + 3)}{x^{2} + 3} dx$

Question Number 116248 Answers: 0 Comments: 0

calculate ∫_(−∞) ^∞ ((arctan(2+x^2 ))/(x^2 −x +1))dx

$calculate \int_{- \infty}^{\infty} \frac{\arctan (2 + x^{2})}{x^{2} - x + 1} dx$

Question Number 116247 Answers: 0 Comments: 0

find the value of I =∫_0 ^∞ ((ch(cos(2x)))/(x^2 +9))dx and J =∫_0 ^∞ ((cos(ch(2x)))/(x^2 +9))dx

$find the value of I = \int_{0}^{\infty} \frac{ch (\cos (2 x))}{x^{2} + 9} dx and$ $J = \int_{0}^{\infty} \frac{\cos (ch (2 x))}{x^{2} + 9} dx$

Question Number 116245 Answers: 3 Comments: 0

calculate ∫_1 ^∞ (dx/((2x^2 −1)^5 ))

$calculate \int_{1}^{\infty} \frac{dx}{{({2 x}^{2} - 1)}^{5}}$

Question Number 116237 Answers: 2 Comments: 0

∫ (√(5cos^2 x+4)) dx ?

$\int \sqrt{5 \cos^{2} x + 4} dx ?$

Question Number 116231 Answers: 1 Comments: 0

∫ sec x tan x (√(tan^2 x−3)) dx ?

$\int \sec x \tan x \sqrt{\tan^{2} x - 3} dx ?$

Question Number 116216 Answers: 1 Comments: 0

∫_0 ^π ((ln (1+(1/2)cos x))/(cos x)) dx ?

$\underset{0}{\int^{π}} \frac{\ln (1 + \frac{1}{2} \cos x)}{\cos x} dx ?$

Question Number 116162 Answers: 1 Comments: 0

Σ_(n=0) ^∞ ((2n+1)/(16^n (n^2 +3n+2))) (((2n)),(n) )^2 =(8/(3π)) m.n.july 1970.

$\underset{n = 0}{\sum^{\infty}} \frac{2 n + 1}{16^{n} (n^{2} + 3 n + 2)} {(\begin{matrix} 2 n \\ n \end{matrix})}^{2} = \frac{8}{3 π}$ $m . n . j u l y 1970 .$

Question Number 116196 Answers: 6 Comments: 0

please solve : ∫_0 ^( (π/4)) tan^9 (x)dx =???

$p l e a s e s o l v e :$ $\int_{0}^{\frac{π}{4}} {t a n}^{9} (x) d x = ? ? ?$

Question Number 116112 Answers: 2 Comments: 0

show that ∫_( 0) ^( ∞) ((lnx)/(1+x^2 ))dx = 0

$show that$ $\int_{0}^{\infty} \frac{lnx}{1 + x^{2}} dx = 0$

Question Number 116123 Answers: 0 Comments: 0

Study according to the values of the real α the convergence of the integral ∫_α ^(+∞) ((ln∣x∣)/( ((x(x+1)))^(1/3) ))dx

$Study according to the values of$ $the real α the convergence of the$ $integral \int_{α}^{+ \infty} \frac{l n ∣ x ∣}{\sqrt[3]{x (x + 1)}} d x$

Question Number 116098 Answers: 0 Comments: 0

1)calculate f(x)=∫_0 ^(2π) (dθ/(x^2 −2x cosθ +1)) 0<θ<(π/2) 2)explicite ∫_0 ^(2π) ((cosθ)/((x^2 −2xcosθ +1)^2 ))dθ

$1) calculate f (x) = \int_{0}^{2 π} \frac{d θ}{x^{2} - 2 x \cos θ + 1} 0 < θ < \frac{π}{2}$ $2) explicite \int_{0}^{2 π} \frac{\cos θ}{{(x^{2} - 2 xcos θ + 1)}^{2}} d θ$

Question Number 116097 Answers: 3 Comments: 0

calculate ∫_0 ^∞ ((lnx)/(x^4 +1))dx

$calculate \int_{0}^{\infty} \frac{lnx}{x^{4} + 1} dx$

Question Number 116096 Answers: 1 Comments: 0

find ∫_0 ^∞ ((lnx)/(x^2 −i))dx (i=(√(−1)))

$find \int_{0}^{\infty} \frac{lnx}{x^{2} - i} dx (i = \sqrt{- 1})$

Question Number 116016 Answers: 1 Comments: 0

∫_(−1) ^1 (dx/( (√(6+x−x^2 )))) ?

$\underset{- 1}{\int^{1}} \frac{d x}{\sqrt{6 + x - x^{2}}} ?$

Question Number 116014 Answers: 1 Comments: 0

...nice calculus ... prove : i:∫_0 ^( ∞) ((ln(x))/((1+x^(√2) )^(√2) )) =0 ✓ ii: ∫_0 ^( ∞) (dx/((1+x^(1+(√2)) )^(1+(√2)) )) =(1/( (√2))) ✓ iii: ∫_0 ^( (π/2)) ln(x^2 +ln^2 (cos(x)))dx=πln(ln(2))✓ ... m.n. july.1970...

$. . . n i c e c a l c u l u s . . .$ $p r o v e :$ $i : \int_{0}^{\infty} \frac{l n (x)}{{(1 + x^{\sqrt{2}})}^{\sqrt{2}}} = 0 ✓$ $i i : \int_{0}^{\infty} \frac{d x}{{(1 + x^{1 + \sqrt{2}})}^{1 + \sqrt{2}}} = \frac{1}{\sqrt{2}} ✓$ $i i i : \int_{0}^{\frac{π}{2}} l n (x^{2} + {l n}^{2} (c o s (x))) d x = π l n (l n (2)) ✓$ $. . . m . n . j u l y . 1970 . . .$

Question Number 116000 Answers: 0 Comments: 0

U(n)=∫_0 ^∞ ((1−tanh x)/( ((tanh x))^(1/n) ))dx another way?

$U (n) = \int_{0}^{\infty} \frac{1 - \tanh x}{\sqrt[n]{\tanh x}} d x$ $a n o t h e r w a y ?$

Question Number 115974 Answers: 0 Comments: 0

∫((e^(3x) −e^x )/(x(e^(3x) +1)(e^x +1)))dx = ?

$\int \frac{e^{3 x} - e^{x}}{x (e^{3 x} + 1) (e^{x} + 1)} d x = ?$

Question Number 115927 Answers: 2 Comments: 0

calculate ∫_1 ^(+∞) (dx/((4x^2 −1)^3 ))

$calculate \int_{1}^{+ \infty} \frac{dx}{{({4 x}^{2} - 1)}^{3}}$

Question Number 115920 Answers: 4 Comments: 0

prove that :: ∫_0 ^( ∞) (tanh^a (x) −tanh^b (x))dx =^(???) ((ψ(((b+1)/2))−ψ(((a+1)/2)))/2) m.n.july.1970

$p r o v e t h a t ::$ $\int_{0}^{\infty} ({t a n h}^{a} (x) - {t a n h}^{b} (x)) d x$ $\overset{? ? ?}{=} \frac{ψ (\frac{b + 1}{2}) - ψ (\frac{a + 1}{2})}{2}$ $m . n . j u l y . 1970$

Question Number 115896 Answers: 2 Comments: 0

∫ ((sec^4 x dx)/( (√(tan^3 x)))) =?

$\int \frac{\sec^{4} x d x}{\sqrt{\tan^{3} x}} = ?$

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