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IntegrationQuestion and Answers: Page 75

Question Number 143230 Answers: 2 Comments: 0

Σ_(n=1) ^∞ (x^(3n+1) /(3n+1))=?

$\underset{n = 1}{\sum^{\infty}} \frac{x^{3 n + 1}}{3 n + 1} = ?$

Question Number 143219 Answers: 0 Comments: 1

Question Number 143210 Answers: 1 Comments: 0

∫_0 ^1 ((7^(x+1) +3^(x+1) )/(x+1))dx

$\int_{0}^{1} \frac{7^{x + 1} + 3^{x + 1}}{x + 1} d x$

Question Number 143192 Answers: 0 Comments: 0

Question Number 143190 Answers: 1 Comments: 2

∫_R (e^(its) /(s+3))ds

$\int_{R} \frac{e^{its}}{s + 3} ds$

Question Number 143178 Answers: 0 Comments: 2

∫_1 ^∞ ((x2^x +7)/(3^x +lnx+1))dx

$\int_{1}^{\infty} \frac{{x 2}^{x} + 7}{3^{x} + lnx + 1} dx$

Question Number 143163 Answers: 0 Comments: 0

∫_(1/x) ^x^2 (dt/( (√(1+t^3 )))) =?

$\int_{\frac{1}{x}}^{x^{2}} \frac{d t}{\sqrt{1 + t^{3}}} = ?$

Question Number 143142 Answers: 1 Comments: 0

∫((x^2 −1)/(x^2 +1))∙(1/( (√(1+x^4 ))))dx

$\int \frac{x^{2} - 1}{x^{2} + 1} \cdot \frac{1}{\sqrt{1 + x^{4}}} dx$

Question Number 143098 Answers: 1 Comments: 0

.....Prove.... Σ_(n=1) ^∞ ((1/(sinh(πn))))^2 =(1/6) −(1/(2π)) ... ......

$. . . . . P r o v e . . . .$ $\underset{n = 1}{\sum^{\infty}} {(\frac{1}{s i n h (π n)})}^{2} = \frac{1}{6} - \frac{1}{2 π} . . .$ $. . . . . .$

Question Number 143094 Answers: 1 Comments: 0

Question Number 143087 Answers: 2 Comments: 0

Question Number 143083 Answers: 1 Comments: 0

calculate Ψ(a,b)=∫_0 ^∞ (e^(−ax^2 ) /((x^2 +b^2 )^2 ))dx with a>0 and b>0

$c a l c u l a t e Ψ (a, b) = \int_{0}^{\infty} \frac{e^{- {a x}^{2}}}{{(x^{2} + b^{2})}^{2}} d x$ $w i t h a > 0 a n d b > 0$

Question Number 143082 Answers: 2 Comments: 0

calculate f(a,b)=∫_0 ^∞ (e^(−ax^2 ) /(x^2 +b^2 ))dx with a>0 and b>0

$c a l c u l a t e f (a, b) = \int_{0}^{\infty} \frac{e^{- {a x}^{2}}}{x^{2} + b^{2}} d x$ $w i t h a > 0 a n d b > 0$

Question Number 143081 Answers: 2 Comments: 0

calculate ∫_0 ^∞ xe^(−x^2 ) arctanx dx

$c a l c u l a t e \int_{0}^{\infty} {x e}^{- x^{2}} a r c t a n x d x$

Question Number 143080 Answers: 2 Comments: 0

calculate ∫_0 ^∞ ((arctan(x^2 ))/(1+x^2 ))dx

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

Question Number 143071 Answers: 2 Comments: 0

∫_0 ^(π/4) ((8dx)/(tgx+1))

$\int_{0}^{\frac{π}{4}} \frac{8 d x}{t g x + 1}$

Question Number 143051 Answers: 1 Comments: 0

_(∗∗∗∗∗) :: Lobachevsky Integral ::_(∗∗∗∗∗) 𝛗:=∫_0 ^( ∞) ((sin^2 ( tan(x)))/x^( 2) )dx=^? (π/2) ..........

$_{* * * * *} :: L o b a c h e v s k y I n t e g r a l : :_{* * * * *}$ $ϕ := \int_{0}^{\infty} \frac{s {i n}^{2} (t a n (x))}{x^{2}} d x \overset{?}{=} \frac{π}{2}$ $. . . . . . . . . .$

Question Number 142990 Answers: 2 Comments: 0

find ∫_0 ^∞ (e^(−x^2 ) /((3+x^2 )^2 ))dx

$find \int_{0}^{\infty} \frac{e^{- x^{2}}}{{(3 + x^{2})}^{2}} dx$

Question Number 142989 Answers: 2 Comments: 0

calculate ∫_0 ^∞ (e^(−3x^2 ) /(1+x^2 ))dx

$calculate \int_{0}^{\infty} \frac{e^{- {3 x}^{2}}}{1 + x^{2}} dx$

Question Number 142983 Answers: 0 Comments: 0

Question Number 142917 Answers: 1 Comments: 0

∫(sin^7 (x))dx

$\int (\sin^{7} (x)) dx$

Question Number 142910 Answers: 2 Comments: 0

Question Number 142900 Answers: 0 Comments: 3

Question Number 142893 Answers: 1 Comments: 0

.....mathematical .....analysis...... f ∈ C [0,1] and ∫_0 ^( 1) x^n f(x)dx=(1/(n+2)) , n∈N prove f(x):=x .....

$. . . . . m a t h e m a t i c a l . . . . . a n a l y s i s . . . . . .$ $f \in C [0, 1] a n d \int_{0}^{1} x^{n} f (x) d x = \frac{1}{n + 2}, n \in N$ $p r o v e f (x) := x . . . . .$

Question Number 142875 Answers: 1 Comments: 0

Prove that ζ(s)=Π_(prime) (1/(1−p^(−s) ))

$P r o v e t h a t ζ (s) = \prod_{p r i m e} \frac{1}{1 - p^{- s}}$

Question Number 142805 Answers: 0 Comments: 0

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