Question and Answers Forum

1) calculate ∫_(−∞) ^(+∞) ((cos(αx^n ))/(x^2 +x +1)) dx with n integr natural 2) find the value of ∫_(−∞) ^∞ ((cos( α x^(2n) ))/(x^2 +x +1))dx 3) calculate ∫_(−∞) ^(+∞) ((cos(π x^3 ))/(x^2 +x +1)) dx

$1) c a l c u l a t e \int_{- \infty}^{+ \infty} \frac{c o s (α x^{n})}{x^{2} + x + 1} d x w i t h n i n t e g r$ $n a t u r a l$ $2) f i n d t h e v a l u e o f \int_{- \infty}^{\infty} \frac{c o s (α x^{2 n})}{x^{2} + x + 1} d x$ $3) c a l c u l a t e \int_{- \infty}^{+ \infty} \frac{c o s (π x^{3})}{x^{2} + x + 1} d x$

Question Number 34562 Answers: 1 Comments: 1

find the value of ∫_0 ^1 ((arctanx)/((1+x^2 )^2 )) dx

$f i n d t h e v a l u e o f \int_{0}^{1} \frac{a r c t a n x}{{(1 + x^{2})}^{2}} d x$

Question Number 34561 Answers: 0 Comments: 1

find the value of ∫_0 ^(+∞) ((arctan(x))/((1+x^2 )^2 )) dx

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

Question Number 34985 Answers: 1 Comments: 0

Question Number 34421 Answers: 0 Comments: 1

let A = ∫_(−∞) ^(+∞) (dx/(x^2 −j)) with j=e^(i((2π)/3)) extract ReA and Im(A) and calculste its values.

$l e t A = \int_{- \infty}^{+ \infty} \frac{d x}{x^{2} - j} w i t h j = e^{i \frac{2 π}{3}}$ $e x t r a c t R e A a n d I m (A) a n d c a l c u l s t e i t s v a l u e s .$

Question Number 34320 Answers: 0 Comments: 2

calculate ∫_(−∞) ^(+∞) (dx/(x^2 +1 −i))

$c a l c u l a t e \int_{- \infty}^{+ \infty} \frac{d x}{x^{2} + 1 - i}$

Question Number 34316 Answers: 0 Comments: 0

find a eajivalent of u_n = ∫_0 ^∞ e^(−(t/n)) arcctant dt .

$f i n d a e a j i v a l e n t o f$ $u_{n} = \int_{0}^{\infty} e^{- \frac{t}{n}} a r c c t a n t d t .$

Question Number 34315 Answers: 0 Comments: 2

1) find F(x)= ∫_0 ^(+∞) ((e^(−at) −e^(−bt) )/t)sin(xt)dt with a>0 ,b>0 .

$1) f i n d F (x) = \int_{0}^{+ \infty} \frac{e^{- a t} - e^{- b t}}{t} s i n (x t) d t$ $w i t h a > 0, b > 0 .$

Question Number 34314 Answers: 0 Comments: 1

let f(x)= ∫_0 ^(+∞) ((1−cos(xt))/t^2 ) e^(−t) dt calculate f(x) .

$l e t f (x) = \int_{0}^{+ \infty} \frac{1 - c o s (x t)}{t^{2}} e^{- t} d t$ $c a l c u l a t e f (x) .$

Question Number 34312 Answers: 0 Comments: 1

calculate I = ∫∫_D x^3 dxdy on the domain D ={(x,y)∈R^2 /1≤x≤2 , x^2 −y^2 −1≥0}

$c a l c u l a t e I = \int \int_{D} x^{3} d x d y o n t h e d o m a i n$ $D = {(x, y) \in R^{2} / 1 ⩽ x ⩽ 2, x^{2} - y^{2} - 1 ⩾ 0}$

Question Number 34308 Answers: 0 Comments: 0

let I = ∫_0 ^(+∞) (((1+x)^(−(1/4)) −(1+x)^(−(3/4)) )/x)dx prove that I isconvergent and find its value .

$l e t I = \int_{0}^{+ \infty} \frac{{(1 + x)}^{- \frac{1}{4}} - {(1 + x)}^{- \frac{3}{4}}}{x} d x$ $p r o v e t h a t I i s c o n v e r g e n t a n d f i n d i t s v a l u e .$

Question Number 34298 Answers: 0 Comments: 2

let A_ = ∫_0 ^∞ e^(−x) cos[x]dx and B = ∫_0 ^∞ e^(−[x]) cosxdx calculate A−B .

$l e t A_{} = \int_{0}^{\infty} e^{- x} c o s [x] d x a n d B = \int_{0}^{\infty} e^{- [x]} c o s x d x$ $c a l c u l a t e A - B .$

Question Number 34297 Answers: 1 Comments: 1

find ∫_(−∞) ^(+∞) e^(−z t^2 ) dt with z=r e^(iθ) ∈ C .

$f i n d \int_{- \infty}^{+ \infty} e^{- z t^{2}} d t w i t h z = r e^{i θ} \in C .$

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