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IntegrationQuestion and Answers: Page 47

Question Number 164974 Answers: 1 Comments: 0

∫_0 ^( 1) (( ln( 1− x ).ln(x ) )/x^( (3/2)) )dx=^? π^( 2) −8ln(2 ) −−− m.n −−−

$\int_{0}^{1} \frac{\ln (1 - x) . \ln (x)}{x^{\frac{3}{2}}} d x \overset{?}{=} π^{2} - 8 \ln (2)$ $- - - m . n - - -$

Question Number 164973 Answers: 1 Comments: 0

Question Number 164944 Answers: 1 Comments: 0

Ω = ∫_0 ^( ∞) e^( − (√x) ) .ln ((x)^(1/4) )dx =? −−−−−−−−−

$Ω = \int_{0}^{\infty} e^{- \sqrt{x}} . l n (\sqrt[4]{x}) d x = ?$ $- - - - - - - - -$

Question Number 164929 Answers: 3 Comments: 0

∫_(−2) ^2 [x]dx=?

$\underset{- 2}{\int^{2}} [x] d x = ?$

Question Number 164904 Answers: 0 Comments: 0

∫_0 ^∞ ((cos^(−1) .(x))/(In ((x) − 3^((x^2 −1)) ))) dx {z.a}

$\int_{0}^{\infty} \frac{\cos^{- 1} . (x)}{I n ((x) - 3^{(x^{2} - 1)})} d x$ ${z . a}$

Question Number 164854 Answers: 1 Comments: 0

Evaluate the Integral; [∫_0 ^∞ ((x^2 − 1)/(1−x)) dx =??] ^({Z.A})

$Evaluate the Integral;$ $[\int_{0}^{\infty} \frac{x^{2} - 1}{1 - x} d x = ? ?]$ $^{{Z . A}}$

Question Number 164853 Answers: 0 Comments: 0

Ω = ∫_0 ^( 1) (( ln(1+x ).ln(x))/(1−x)) dx

$Ω = \int_{0}^{1} \frac{l n (1 + x) . l n (x)}{1 - x} d x$

Question Number 164809 Answers: 2 Comments: 0

1) ∫((x)^(1/3) /( (√x)+(x)^(1/4) ))=? 2) ∫(x/((x^2 +2x+2)^2 ))=?

$1) \int \frac{\sqrt[3]{x}}{\sqrt{x} + \sqrt[4]{x}} = ?$ $2) \int \frac{x}{{(x^{2} + 2 x + 2)}^{2}} = ?$

Question Number 164719 Answers: 0 Comments: 0

Question Number 164686 Answers: 1 Comments: 0

∫36x^2 (2x+3)^(−7) dx

$\int 36 x^{2} {(2 x + 3)}^{- 7} d x$

Question Number 164685 Answers: 1 Comments: 0

∫4x^2 (1−x)^3 dx

$\int 4 x^{2} {(1 - x)}^{3} d x$

Question Number 164684 Answers: 1 Comments: 0

∫24(2x−1)^(−3) dx

$\int 24 {(2 x - 1)}^{- 3} d x$

Question Number 164683 Answers: 1 Comments: 0

∫(x^2 /((x+7)^4 ))dx

$\int \frac{x^{2}}{{(x + 7)}^{4}} d x$

Question Number 164682 Answers: 1 Comments: 0

∫27x^2 (√(3x−2)) dx

$\int 27 x^{2} \sqrt{3 x - 2} d x$

Question Number 164681 Answers: 1 Comments: 0

∫ (−8x(√(3−2x)) )dx

$\int (- 8 x \sqrt{3 - 2 x}) d x$

Question Number 164672 Answers: 1 Comments: 0

Question Number 164605 Answers: 1 Comments: 0

Question Number 164600 Answers: 3 Comments: 0

Question Number 164598 Answers: 0 Comments: 0

Prove that; ∫_(−∞) ^∞ y tan x + y^3 tan x dx = undefined

$Prove that;$ $\int_{- \infty}^{\infty} y t a n x + y^{3} t a n x d x = u n d e f i n e d$

Question Number 164590 Answers: 1 Comments: 0

∫ ((In(x^2 .e^(cos2) ))/x) dx

$\int \frac{In (x^{2} . e^{c o s 2})}{x} dx$

Question Number 164589 Answers: 0 Comments: 0

∫ A.^5 (√(x^3 )) dx

$\int A .^{5} \sqrt{x^{3}} dx$

Question Number 164582 Answers: 0 Comments: 0

Question Number 164419 Answers: 1 Comments: 0

please help me prouve that ∫_0 ^1 ((lnt)/(t^2 −1))dt=(π^2 /8)

$p l e a s e h e l p m e$ $p r o u v e t h a t \int_{0}^{1} \frac{l n t}{t^{2} - 1} d t = \frac{π^{2}}{8}$

Question Number 164395 Answers: 2 Comments: 0

Question Number 164328 Answers: 2 Comments: 0

solve Σ_(n=0) ^∞ (( cos^(2n) (x))/(n!)) = (e)^(1/4) ■ −−−−−−−

$s o l v e$ $\underset{n = 0}{\sum^{\infty}} \frac{{c o s}^{2 n} (x)}{n!} = \sqrt[4]{e} ◼$ $- - - - - - -$

Question Number 164242 Answers: 0 Comments: 0

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