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IntegrationQuestion and Answers: Page 102

Question Number 130759 Answers: 3 Comments: 0

...nice calculus ... find : φ =∫_0 ^( ∞) (x^2 ln(1+e^x )−x^3 )dx

$. . . n i c e c a l c u l u s . . .$ $f i n d : ϕ = \int_{0}^{\infty} (x^{2} l n (1 + e^{x}) - x^{3}) d x$

Question Number 130738 Answers: 2 Comments: 0

∫_( 1) ^( cosh x) (√(t^2 −1)) dt = ?

$\int_{1}^{\cosh x} \sqrt{t^{2} - 1} dt = ?$

Question Number 130725 Answers: 1 Comments: 0

find ∫_0 ^1 (x^2 /( (√(x^4 +1))))dx

$find \int_{0}^{1} \frac{x^{2}}{\sqrt{x^{4} + 1}} dx$

Question Number 130693 Answers: 3 Comments: 0

... nice calculus... evaluate :: =∫_0 ^( ∞) ((sin(x))/(e^x −1)) dx =?? ....................

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

Question Number 130698 Answers: 0 Comments: 0

What exact value of cot (1120°−x) where csc x = 3

$What exact value of \cot (1120 ° - x)$ $where \csc x = 3$

Question Number 130684 Answers: 0 Comments: 0

1)calculate ∫ (dx/((x−1)(x−2)....(x−n))) ( n integr natural) 2) find the value of U_n =∫_(n+1) ^∞ (dx/((x−1)(x−2)....(x−n)))

$1) calculate \int \frac{dx}{(x - 1) (x - 2) . . . . (x - n)} (n integr natural)$ $2) find the value of U_{n} = \int_{n + 1}^{\infty} \frac{dx}{(x - 1) (x - 2) . . . . (x - n)}$

Question Number 130678 Answers: 1 Comments: 0

∫ ((3(√x))/(x−1)) dx ?

$\int \frac{3 \sqrt{x}}{x - 1} d x ?$

Question Number 130676 Answers: 1 Comments: 0

∫_0 ^( 1) ((ln (1+x+x^2 ))/x) dx ?

$\int_{0}^{1} \frac{\ln (1 + x + x^{2})}{x} d x ?$

Question Number 130626 Answers: 0 Comments: 0

∫_0 ^( ∞) ((x^4 tan^(−1) (x))/(1+x^6 ))dx

$\int_{0}^{\infty} \frac{x^{4} \tan^{- 1} (x)}{1 + x^{6}} dx$

Question Number 130616 Answers: 2 Comments: 0

∫ (dx/(1−k.sin x)) ? where ∣k∣<1

$\int \frac{dx}{1 - k . \sin x} ? where ∣ k ∣< 1$

Question Number 130598 Answers: 2 Comments: 0

∫_0 ^( ∞) ((x^2 tan^(−1) (x))/(1+x^6 ))dx

$\int_{0}^{\infty} \frac{x^{2} \tan^{- 1} (x)}{1 + x^{6}} dx$

Question Number 130594 Answers: 2 Comments: 0

∫_0 ^( ∞) (x^n /(1+x^6 ))dx

$\int_{0}^{\infty} \frac{x^{n}}{1 + x^{6}} dx$

Question Number 130560 Answers: 2 Comments: 0

Question Number 130556 Answers: 0 Comments: 0

∫_0 ^(π/2) ((xcosx)/(1+sin^2 x))dx

$\int_{0}^{\frac{π}{2}} \frac{xcosx}{1 + \sin^{2} x} dx$

Question Number 130544 Answers: 2 Comments: 0

∫ ((sin^2 x sec^2 x +2(√(1−x^2 )) tan x sin^(−1) x)/( (√(1−x^2 )) (1+tan^2 x))) dx?

$\int \frac{\sin^{2} x \sec^{2} x + 2 \sqrt{1 - x^{2}} \tan x \sin^{- 1} x}{\sqrt{1 - x^{2}} (1 + \tan^{2} x)} d x ?$

Question Number 130534 Answers: 1 Comments: 0

let f(x)=x^7 arctan(2x) 1)calculate f^((4)) (0) and f^((7)) (0) 2) calculate f^((5)) (1)

$let f (x) = x^{7} \arctan (2 x)$ $1) calculate f^{(4)} (0) and f^{(7)} (0)$ $2) calculate f^{(5)} (1)$

Question Number 130533 Answers: 1 Comments: 0

find ∫ ((x^3 +5)/(x^4 +2x^2 −3))dx

$find \int \frac{x^{3} + 5}{x^{4} + {2 x}^{2} - 3} dx$

Question Number 130532 Answers: 0 Comments: 0

find f(α)=∫_0 ^∞ ((arctan(1+αx))/(4+x^2 ))dx (α>0) and determine the value of ∫_0 ^∞ ((arctan(1+2x))/(x^2 +4))dx

$find f (α) = \int_{0}^{\infty} \frac{\arctan (1 + α x)}{4 + x^{2}} dx (α > 0)$ $and determine the value of \int_{0}^{\infty} \frac{\arctan (1 + 2 x)}{x^{2} + 4} dx$

Question Number 130531 Answers: 1 Comments: 0

find ∫_0 ^1 arctan(x^2 +x+1)dx

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

Question Number 130530 Answers: 0 Comments: 2

find ∫_0 ^∞ ((xsin(2x))/((x^2 +x+1)^2 ))dx

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

Question Number 130529 Answers: 1 Comments: 0

calvulste ∫_0 ^(2π) ((cos(2x))/(3+cosx))dx

$calvulste \int_{0}^{2 π} \frac{\cos (2 x)}{3 + cosx} dx$

Question Number 130528 Answers: 1 Comments: 0

calculate ∫_2 ^∞ (dx/((x^2 −1)^5 ))

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

Question Number 130512 Answers: 2 Comments: 2

∫xe^(1/(2x)) dx=?

$\int x e^{\frac{1}{2 x}} d x = ?$

Question Number 130536 Answers: 2 Comments: 0

calculate ∫_0 ^(2π) ln(x^2 −2xcosθ +1)dθ

$calculate \int_{0}^{2 π} \ln (x^{2} - 2 xcos θ + 1) d θ$

Question Number 130486 Answers: 1 Comments: 0

∫_0 ^( x) ((cos t ((sin^3 t))^(1/4) )/((sin x−sin t)^(3/4) )) dt ?

$\int_{0}^{x} \frac{\cos t \sqrt[4]{\sin^{3} t}}{{(\sin x - \sin t)}^{3 / 4}} d t ?$

Question Number 130485 Answers: 2 Comments: 0

ϝ = ∫_0 ^( ∞) x^(5 ) ln (x)cos (x)e^(−x) dx ?

$ϝ = \int_{0}^{\infty} x^{5} \ln (x) \cos (x) e^{- x} d x ?$

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