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IntegrationQuestion and Answers: Page 113

Question Number 126715 Answers: 0 Comments: 0

Question Number 126714 Answers: 0 Comments: 0

Question Number 126710 Answers: 1 Comments: 0

∫ln(x)e^x^2 dx ???

$\int l n (x) e^{x^{2}} d x ? ? ?$

Question Number 126661 Answers: 0 Comments: 3

... calculus... evaluate :: Φ=∫_0 ^( 1) (((1+x^4 ln(x))/(1+x^6 )))dx=?

$. . . c a l c u l u s . . .$ $e v a l u a t e ::$ $Φ = \int_{0}^{1} (\frac{1 + x^{4} l n (x)}{1 + x^{6}}) d x = ?$

Question Number 126604 Answers: 1 Comments: 0

∫ (dx/((1−x^2 ) ((2x^2 −1))^(1/4) )) ?

$\int \frac{d x}{(1 - x^{2}) \sqrt[4]{2 x^{2} - 1}} ?$

Question Number 126601 Answers: 0 Comments: 0

∫_(1/n) ^( (3/n)) log(Γ(x))dx

$\int_{\frac{1}{n}}^{\frac{3}{n}} \log (Γ (x)) dx$

Question Number 126586 Answers: 3 Comments: 0

∫ ((sin x)/(cos x−sin x)) dx ?

$\int \frac{\sin x}{\cos x - \sin x} d x ?$

Question Number 126577 Answers: 2 Comments: 0

∫_0 ^3 (((3−x)x^2 ))^(1/3) dx =?

$\underset{0}{\int^{3}} \sqrt[3]{(3 - x) x^{2}} d x = ?$

Question Number 126571 Answers: 1 Comments: 0

∫ ((√(tan x))/( (√(tan^2 x−1)))) dx ?

$\int \frac{\sqrt{\tan x}}{\sqrt{\tan^{2} x - 1}} d x ?$

Question Number 126529 Answers: 0 Comments: 1

Question Number 126510 Answers: 4 Comments: 0

∫ (dx/((x−2)(√(x^2 +4x+8)))) ?

$\int \frac{d x}{(x - 2) \sqrt{x^{2} + 4 x + 8}} ?$

Question Number 126502 Answers: 1 Comments: 0

∫ (dx/( (√(sin^5 x cos^7 x)))) ?

$\int \frac{d x}{\sqrt{\sin^{5} x \cos^{7} x}} ?$

Question Number 126494 Answers: 1 Comments: 0

calculate ∫_0 ^∞ ((sinx)/(x(x^4 +1)))dx

$calculate \int_{0}^{\infty} \frac{sinx}{x (x^{4} + 1)} dx$

Question Number 126493 Answers: 2 Comments: 0

calculate ∫_0 ^∞ (dx/((x^4 +1)^2 ))

$calculate \int_{0}^{\infty} \frac{dx}{{(x^{4} + 1)}^{2}}$

Question Number 126465 Answers: 1 Comments: 1

... nice calculus... Evaluate ... φ = ∫_0 ^( 1) ((sin(ln(x))−ln(x))/(ln^2 (x)))dx Ans :: ln((√2) )+(π/4) −1 ...

$. . . n i c e c a l c u l u s . . .$ $E v a l u a t e . . .$ $ϕ = \int_{0}^{1} \frac{s i n (l n (x)) - l n (x)}{{l n}^{2} (x)} d x$ $A n s :: l n (\sqrt{2}) + \frac{π}{4} - 1 . . .$

Question Number 126427 Answers: 1 Comments: 0

lim_(x→−3) ((∣x+3∣)/(x+3)) show right and left side limit??

$l i \underset{x \to - 3}{m} \frac{∣ x + 3 ∣}{x + 3} s h o w r i g h t a n d l e f t s i d e$ $l i m i t ? ?$

Question Number 126383 Answers: 1 Comments: 0

Evaluate Ω if Ω = ∫_0 ^( ∞) ((cos(mx))/(x^4 +x^2 +1))dx

$Evaluate Ω if$ $Ω = \int_{0}^{\infty} \frac{\cos (mx)}{x^{4} + x^{2} + 1} dx$

Question Number 126369 Answers: 1 Comments: 0

∫ ((tan(x))/x) dx

$\int \frac{\tan (x)}{x} dx$

Question Number 126344 Answers: 1 Comments: 0

evaluate :: ∫_(−1) ^( 0) (dx/( ((1+x^3 ))^(1/3) )) =?

$e v a l u a t e :: \int_{- 1}^{0} \frac{d x}{\sqrt[3]{1 + x^{3}}} = ?$

Question Number 126316 Answers: 0 Comments: 2

∫_( (√2)) ^(2e^(√2) ) ln (((e^x +e^(−x) )/(9(√x))))dx ?

$\underset{\sqrt{2}}{\int^{2 e^{\sqrt{2}}}} \ln (\frac{e^{x} + e^{- x}}{9 \sqrt{x}}) d x ?$

Question Number 126315 Answers: 1 Comments: 0

∫(1/dx)=?

$\int \frac{1}{d x} = ?$

Question Number 126314 Answers: 2 Comments: 0

∫ (dx/((1+x^2 )(√(1−x^2 )))) ?

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

Question Number 126298 Answers: 3 Comments: 0

∫_( 0) ^( (√(ln (π/2)))) xe^x^2 sin (e^x^2 ) dx ?

$\int_{0}^{\sqrt{\ln (π / 2)}} {x e}^{x^{2}} \sin (e^{x^{2}}) d x ?$

Question Number 126323 Answers: 0 Comments: 0

... advanced calculus... prove that ::: ((Γ(((1−x)/2))Γ(x))/(Γ((x/2)))) =^(???) ((2^(x−1) (√π))/(cos(((πx)/2))))

$. . . a d v a n c e d c a l c u l u s . . .$ $p r o v e t h a t :::$ $\frac{Γ (\frac{1 - x}{2}) Γ (x)}{Γ (\frac{x}{2})} \overset{? ? ?}{=} \frac{2^{x - 1} \sqrt{π}}{c o s (\frac{π x}{2})}$

Question Number 126349 Answers: 0 Comments: 1

...nice calculus... calculate ::: Ω=^(???) ∫_0 ^( ∞) e^( −t) t^( 2) j_0 ( t )dt where : j_((v)) (x)=x^v Σ_(n=0) ^( ∞) (((−1)^n x^(2n) )/(2^(2n+v) n!Γ(n+v+1))) ::: Bessel function of the first type of order v ... j_v (x) is convergent (why?): ∀x∈R...

$. . . n i c e c a l c u l u s . . .$ $c a l c u l a t e :::$ $Ω \overset{? ? ?}{=} \int_{0}^{\infty} e^{- t} t^{2} j_{0} (t) d t$ $w h e r e : j_{(v)} (x) = x^{v} \underset{n = 0}{\sum^{\infty}} \frac{{(- 1)}^{n} x^{2 n}}{2^{2 n + v} n! Γ (n + v + 1)}$ $::: B e s s e l f u n c t i o n o f$ $t h e f i r s t t y p e o f o r d e r v . . .$ $j_{v} (x) i s c o n v e r g e n t (w h y ?) : \forall x \in R . . .$

Question Number 126274 Answers: 2 Comments: 0

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