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let f(x) =∫_0 ^∞ (dt/((x^2 +t^2 )^2 )) with x>0 1) find a explicit form of (x) 2)find also g(x) =∫_0 ^∞ (dt/((x^2 +t^2 )^3 )) 3)find the values of integrals ∫_0 ^∞ (dt/((t^2 +3)^2 )) and ∫_0 ^∞ (dt/((t^2 +3)^3 )) 4) calculate U_θ =∫_0 ^∞ (dt/((t^2 +cos^2 θ)^2 )) with 0<θ<(π/2) 5) find f^((n)) (x) and f^((n)) (0) 6) developp f at integr serie

$l e t f (x) = \int_{0}^{\infty} \frac{d t}{{(x^{2} + t^{2})}^{2}} w i t h x > 0$ $1) f i n d a e x p l i c i t f o r m o f (x)$ $2) f i n d a l s o g (x) = \int_{0}^{\infty} \frac{d t}{{(x^{2} + t^{2})}^{3}}$ $3) f i n d t h e v a l u e s o f i n t e g r a l s \int_{0}^{\infty} \frac{d t}{{(t^{2} + 3)}^{2}} a n d \int_{0}^{\infty} \frac{d t}{{(t^{2} + 3)}^{3}}$ $4) c a l c u l a t e U_{θ} = \int_{0}^{\infty} \frac{d t}{{(t^{2} + {c o s}^{2} θ)}^{2}} w i t h 0 < θ < \frac{π}{2}$ $5) f i n d f^{(n)} (x) a n d f^{(n)} (0)$ $6) d e v e l o p p f a t i n t e g r s e r i e$

Question Number 67006 Answers: 0 Comments: 1

calculae A_n =∫_0 ^∞ (dx/((x^2 +1)^n )) with n integr natural and n>0

$c a l c u l a e A_{n} = \int_{0}^{\infty} \frac{d x}{{(x^{2} + 1)}^{n}} w i t h n i n t e g r n a t u r a l a n d n > 0$

Question Number 67005 Answers: 0 Comments: 1

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

$f i n d \int \frac{x - 2 \sqrt{x^{2} - 1}}{x + 2 \sqrt{x^{2} - 1}} d x$

Question Number 66959 Answers: 0 Comments: 0

Question Number 66938 Answers: 2 Comments: 7

Question Number 66814 Answers: 0 Comments: 0

Let consider an integer serie {a_n x^n } given by a_n = H_n =Σ_(k=1) ^n (1/k) 1) Find out the largest domain D of convergence of that integer serie 2) ∀ x∈D , explicit the sum S(x) of the {a_n x^n } 3) Calculate ∫_(−1) ^1 S(1−x)S(x) dx .

$L e t c o n s i d e r a n i n t e g e r s e r i e {a_{n} x^{n}} g i v e n b y a_{n} = H_{n} = \underset{k = 1}{\sum^{n}} \frac{1}{k}$ $1) F i n d o u t t h e l a r g e s t d o m a i n D o f c o n v e r g e n c e o f t h a t i n t e g e r s e r i e$ $2) \forall x \in D, e x p l i c i t t h e s u m S (x) o f t h e {a_{n} x^{n}}$ $3) C a l c u l a t e \int_{- 1}^{1} S (1 - x) S (x) d x .$

Question Number 66801 Answers: 0 Comments: 3

let f(x) =∫_0 ^2 (√(x+t^2 ))dt with x≥0 1) calculate f(x) 2)calculate g(x) =∫_0 ^2 (dt/(√(x+t^2 ))) 3)find the value[of ∫_0 ^2 (√(4+t^2 ))dt and ∫_0 ^2 (dt/(√(3+t^2 ))) 4) give g^′ (x) at form of integral.

$l e t f (x) = \int_{0}^{2} \sqrt{x + t^{2}} d t w i t h x ⩾ 0$ $1) c a l c u l a t e f (x)$ $2) c a l c u l a t e g (x) = \int_{0}^{2} \frac{d t}{\sqrt{x + t^{2}}}$ $3) f i n d t h e v a l u e [o f \int_{0}^{2} \sqrt{4 + t^{2}} d t a n d \int_{0}^{2} \frac{d t}{\sqrt{3 + t^{2}}}$ $4) g i v e g^{^{'}} (x) a t f o r m o f i n t e g r a l .$

Question Number 66795 Answers: 0 Comments: 3

let f(x) =e^(−x) ln(1+x^2 ) 1) calculate f^((n)) (0) 2) developp f at integr serie

$l e t f (x) = e^{- x} l n (1 + x^{2})$ $1) c a l c u l a t e f^{(n)} (0)$ $2) d e v e l o p p f a t i n t e g r s e r i e$

Question Number 66794 Answers: 0 Comments: 1

calculate ∫_0 ^∞ ((cos(2arctan(2x)))/(9+x^2 ))dx

$c a l c u l a t e \int_{0}^{\infty} \frac{c o s (2 a r c t a n (2 x))}{9 + x^{2}} d x$

Question Number 66793 Answers: 0 Comments: 0

calculate ∫_0 ^1 cos(3arctanx)dx

$c a l c u l a t e \int_{0}^{1} c o s (3 a r c t a n x) d x$

Question Number 66792 Answers: 0 Comments: 1

calculate ∫_0 ^1 cos(2 arctan(x))dx

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

Pg 209 Pg 210 Pg 211 Pg 212 Pg 213 Pg 214 Pg 215 Pg 216 Pg 217 Pg 218

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