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IntegrationQuestion and Answers: Page 235

Question Number 60680 Answers: 0 Comments: 2

study the integral ∫_0 ^1 (x/(ln(1−x)))dx

$s t u d y t h e i n t e g r a l \int_{0}^{1} \frac{x}{l n (1 - x)} d x$

Question Number 60679 Answers: 0 Comments: 1

calculate ∫_0 ^∞ ((ln(1+e^(−x^2 ) ))/(x^2 +4)) dx

$c a l c u l a t e \int_{0}^{\infty} \frac{l n (1 + e^{- x^{2}})}{x^{2} + 4} d x$

Question Number 60678 Answers: 0 Comments: 3

calculate ∫_0 ^1 ((ln(1−x^2 ))/x) dx

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

Question Number 60670 Answers: 1 Comments: 2

Question Number 60675 Answers: 0 Comments: 0

∫_0 ^(π/2) ln[((ln^2 (sin(x)))/(π^2 +ln^2 (sinx)))]((ln(cos(x)))/(tan(x)))dx

$\int_{0}^{\frac{π}{2}} l n [\frac{{l n}^{2} (s i n (x))}{π^{2} + {l n}^{2} (s i n x)}] \frac{l n (c o s (x))}{t a n (x)} d x$

Question Number 60662 Answers: 0 Comments: 0

Question Number 60659 Answers: 1 Comments: 1

find ∫_0 ^1 ln(x)ln(1−x^2 )dx

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

Question Number 60658 Answers: 0 Comments: 1

calculate ∫_0 ^1 ln(x)ln(1−x)ln(1−x^2 )dx

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

Question Number 60637 Answers: 1 Comments: 1

Question Number 60623 Answers: 0 Comments: 0

What are all intregal methods that exist like trigonometry sub. Gaussian method feyman method ?

$W h a t a r e a l l i n t r e g a l m e t h o d s t h a t e x i s t$ $l i k e t r i g o n o m e t r y s u b . G a u s s i a n m e t h o d f e y m a n m e t h o d ?$

Question Number 60621 Answers: 0 Comments: 5

if π is rational then there exists a I_n =(v^(2n) /(n!))∫_0 ^π x^n (x−π)^n sin(x)dx can someone give a easier way to expaned this

$i f π i s r a t i o n a l t h e n t h e r e$ $e x i s t s a I_{n} = \frac{v^{2 n}}{n!} \underset{0}{\int^{π}} x^{n} {(x - π)}^{n} s i n (x) d x$ $c a n s o m e o n e g i v e a e a s i e r w a y t o e x p a n e d t h i s$

Question Number 60631 Answers: 0 Comments: 0

prove that∫_(−∞) ^∞ x^5 e^(−x^2 ) sin(x^3 ) dx=0.25474

$prove that \underset{- \infty}{\int^{\infty}} x^{5} e^{- x^{2}} \sin (x^{3}) dx = 0.25474$

Question Number 60586 Answers: 0 Comments: 1

find ∫_0 ^1 ((ln^2 (x))/((1−x^2 )^2 ))dx

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

Question Number 60534 Answers: 0 Comments: 1

Question Number 60506 Answers: 0 Comments: 1

calculate ∫∫_W ((√(2x^2 +3y^2 ))/(x+y)) dxdy with W ={(x,y)∈R^2 / 0<x<1 and 0<y<1.

$c a l c u l a t e \int \int_{W} \frac{\sqrt{2 x^{2} + 3 y^{2}}}{x + y} d x d y$ $w i t h W = {(x, y) \in R^{2} / 0 < x < 1 a n d 0 < y < 1 .$

Question Number 60498 Answers: 0 Comments: 4

let f(t) =∫_0 ^3 (√(t +x +x^2 ))dx with t ≥(1/4) 1) find a explicit form of f(t) 2) find also g(t) = ∫_0 ^3 (dx/(√(t+x +x^2 ))) 3) calculate ∫_0 ^3 (√(1+x+x^2 ))dx , ∫_0 ^3 (√(2 +x+x^2 ))dx ∫_0 ^3 (dx/(√(2+x +x^2 ))) .

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

Question Number 60595 Answers: 0 Comments: 2

let f(a) =∫_0 ^1 ((ln^2 (x))/((1−ax)^2 )) dx with ∣a∣<1 1) find a explicit form of f(a) 2) determine A(θ) =∫_0 ^1 ((ln^2 (x))/((1−(cosθ)x)^2 ))dx with 0<θ<(π/2)

$l e t f (a) = \int_{0}^{1} \frac{{l n}^{2} (x)}{{(1 - a x)}^{2}} d x w i t h ∣ a ∣< 1$ $1) f i n d a e x p l i c i t f o r m o f f (a)$ $2) d e t e r m i n e A (θ) = \int_{0}^{1} \frac{{l n}^{2} (x)}{{(1 - (c o s θ) x)}^{2}} d x w i t h 0 < θ < \frac{π}{2}$