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IntegrationQuestion and Answers: Page 74

Question Number 143638 Answers: 0 Comments: 2

......Calculus.... 𝛗:=^? ∫_0 ^( 1) ((ln(1−x)ln(x)(ln(((1−x)/x))))/x) dx m.n....

$. . . . . . C a l c u l u s . . . .$ $ϕ : \overset{?}{=} \int_{0}^{1} \frac{l n (1 - x) l n (x) (l n (\frac{1 - x}{x}))}{x} d x$ $m . n . . . .$

Question Number 143628 Answers: 1 Comments: 0

∫_x ^∝ t^(α−1) e^(it) dt=??

$\int_{x}^{\propto} t^{α - 1} e^{i t} d t = ? ?$

Question Number 143622 Answers: 1 Comments: 0

∫_0 ^∝ e^(2arctg(t^2 )) dt

$\int_{0}^{\propto} e^{2 a r c t g (t^{2})} d t$

Question Number 143603 Answers: 2 Comments: 0

.....Calculus..... Ω:=Σ_(n=1) ^∞ (1/(n^k (1+n))) (k≥ 2) ......

$. . . . . C a l c u l u s . . . . .$ $Ω := \underset{n = 1}{\sum^{\infty}} \frac{1}{n^{k} (1 + n)} (k ⩾ 2) . . . . . .$

Question Number 143588 Answers: 3 Comments: 0

Question Number 143570 Answers: 1 Comments: 0

Question Number 143715 Answers: 0 Comments: 0

∫_0 ^(π/4) tanx∙Li(tan^2 x)dx

$\int_{0}^{\frac{π}{4}} tanx \cdot Li (\tan^{2} x) dx$

Question Number 143556 Answers: 0 Comments: 0

∫_0 ^∞ (dx/(x^α (lnx)^β ))

$\int_{0}^{\infty} \frac{dx}{x^{α} {(lnx)}^{β}}$

Question Number 143508 Answers: 3 Comments: 0

..........Calculus........ i: 𝛗_1 :=∫_0 ^( 1) ((ln^2 (1−x).ln(x))/x)dx ii: 𝛗_2 := ∫_0 ^( 1) ((ln^2 (x).ln(1−x))/x) dx iii : 𝛗_3 :=∫_0 ^( 1) ((ln^2 (x).ln(1+x))/x)dx

$. . . . . . . . . . C a l c u l u s . . . . . . . .$ $i : ϕ_{1} := \int_{0}^{1} \frac{{l n}^{2} (1 - x) . l n (x)}{x} d x$ $i i : ϕ_{2} := \int_{0}^{1} \frac{{l n}^{2} (x) . l n (1 - x)}{x} d x$ $i i i : ϕ_{3} := \int_{0}^{1} \frac{{l n}^{2} (x) . l n (1 + x)}{x} d x$

Question Number 143506 Answers: 1 Comments: 0

∫_1 ^∞ (1/(e^(−x) +e^x )) dx=?

$\underset{1}{\int^{\infty}} \frac{1}{e^{- x} + e^{x}} d x = ?$

Question Number 143502 Answers: 0 Comments: 0

Question Number 143487 Answers: 0 Comments: 0

find ∫_0 ^1 ((log(1+t^2 ))/(1+t))dt

$find \int_{0}^{1} \frac{\log (1 + t^{2})}{1 + t} dt$

Question Number 143477 Answers: 0 Comments: 0

∫_0 ^1 e^(2arctg(t^2 )) dt

$\int_{0}^{1} e^{2 a r c t g (t^{2})} d t$

Question Number 143474 Answers: 0 Comments: 0

for all positive integral., u_(n+1) =u_n (u_(n−1) ^2 −2)−u_n u_n =2 and u_1 =2(1/2) prove that : 3log_2 [u_n ]=2^n −1(−1)^n where [x] is the integral part of x

$f o r a l l p o s i t i v e i n t e g r a l .,$ $u_{n + 1} = u_{n} (u_{n - 1}^{2} - 2) - u_{n}$ $u_{n} = 2 a n d u_{1} = 2 \frac{1}{2}$ $p r o v e t h a t : {3 \log}_{2} [u_{n}] = 2^{n} - 1 {(- 1)}^{n}$ $w h e r e [x] i s t h e i n t e g r a l p a r t o f x$