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IntegrationQuestion and Answers: Page 309

Question Number 29439 Answers: 1 Comments: 0

find ∫_0 ^π (dx/(2+cosx)) .

$f i n d \int_{0}^{π} \frac{d x}{2 + c o s x} .$

Question Number 29384 Answers: 0 Comments: 3

Please can it be proven by another means that ∫tan^2 xdx=tanx+x +c

$P l e a s e c a n i t b e p r o v e n b y a n o t h e r$ $m e a n s t h a t$ $\int \tan^{2} x d x = t a n x + x + c$

Question Number 29423 Answers: 0 Comments: 1

Question Number 29311 Answers: 0 Comments: 0

∫(2x^3 −3x^2 +3x−1)^(1/5) dx and limit is from 0 to 1

$\int {(2 x^{3} - 3 x^{2} + 3 x - 1)}^{\frac{1}{5}} d x a n d l i m i t i s f r o m 0 t o 1$

Question Number 29202 Answers: 1 Comments: 0

Find area between by y=1 and y=((1−x^2 )/(1+x^2 )) .

$F i n d a r e a b e t w e e n b y y = 1 a n d$ $y = \frac{1 - x^{2}}{1 + x^{2}} .$

Question Number 29162 Answers: 0 Comments: 1

find find I= ∫_1 ^3 ((∣x−2∣)/((x^2 −4x)^2 ))dx .

$f i n d f i n d I = \int_{1}^{3} \frac{∣ x - 2 ∣}{{(x^{2} - 4 x)}^{2}} d x .$

Question Number 29105 Answers: 0 Comments: 2

Show that: ∫_(−1) ^( 1) (dx/(5 cosh(x) + 13 sinh(x))) = (1/2) log_e (((15e − 10)/(3e + 2)))

$Show that : \int_{- 1}^{1} \frac{dx}{5 \cosh (x) + 13 \sinh (x)} = \frac{1}{2} \log_{e} (\frac{15 e - 10}{3 e + 2})$

Question Number 29079 Answers: 0 Comments: 0

let give w(x)= ∫_0 ^1 ((arcsin(x(1+t^2 )))/(1+t^2 ))dt find w(x).

$l e t g i v e w (x) = \int_{0}^{1} \frac{a r c s i n (x (1 + t^{2}))}{1 + t^{2}} d t f i n d w (x) .$

Question Number 29078 Answers: 0 Comments: 2

let give h(x)= ∫_0 ^1 ((arctan(xt))/(1+t^2 )) find h(x) .

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

Question Number 29077 Answers: 0 Comments: 1

let give g(x)=∫_0 ^∞ ((arctan(x(1+t^2 )))/(1+t^2 ))dt find a simple form of g^′ (x) without integral.

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

Question Number 29076 Answers: 0 Comments: 1

let give f(x)= ∫_0 ^1 ((arctan(x(1+t^2 )))/(1+t^2 ))dt find asimple form of f(x) without integral.

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

Question Number 29043 Answers: 0 Comments: 1

∫tan^− (1−sinx/1+sinx) dx

$\int \tan^{-} (1 - sinx / 1 + sinx) dx$

Question Number 29038 Answers: 0 Comments: 1

find ∫_(−∞) ^(+∞) ((cos(at))/(1+t^4 ))dt.

$f i n d \int_{- \infty}^{+ \infty} \frac{c o s (a t)}{1 + t^{4}} d t .$

Question Number 29028 Answers: 0 Comments: 0

for t>0 and f(t)= (4πt)^(−(n/2)) e^(−(x^2 /(4t))) prove that ∫_R f_t (x)dx=1 ∀t>0.

$f o r t > 0 a n d f (t) = {(4 π t)}^{- \frac{n}{2}} e^{- \frac{x^{2}}{4 t}} p r o v e t h a t$ $\int_{R} f_{t} (x) d x = 1 \forall t > 0 .$

Question Number 29027 Answers: 0 Comments: 0

find ∫∫_D e^(−y) sin(2xy)dxdy with D=[0,1]×[0,+∞[ then find the value of ∫_0 ^∞ ((sin^2 t)/t) e^(−t) dt .

$f i n d \int \int_{D} e^{- y} s i n (2 x y) d x d y w i t h D = [0, 1] \times [0, + \infty [$ $t h e n f i n d t h e v a l u e o f \int_{0}^{\infty} \frac{{s i n}^{2} t}{t} e^{- t} d t .$

Question Number 29018 Answers: 0 Comments: 0

∫ (√(Σ_(n = 0) ^∞ [(−1)^n tan^(2n) (2x)])) dx

$\int \sqrt{\underset{n = 0}{\sum^{\infty}} [{(- 1)}^{n} \tan^{2 n} (2 x)]} d x$

Question Number 29003 Answers: 1 Comments: 1

find ∫_0 ^∞ (dx/(1+x^3 )) .

$f i n d \int_{0}^{\infty} \frac{d x}{1 + x^{3}} .$

Question Number 29002 Answers: 0 Comments: 0

let give 0<p<1 calculate K(p)= ∫_(−∞) ^(+∞) (e^(pt) /(1+e^t ))dt.

$l e t g i v e 0 < p < 1 c a l c u l a t e K (p) = \int_{- \infty}^{+ \infty} \frac{e^{p t}}{1 + e^{t}} d t .$

Question Number 29001 Answers: 0 Comments: 0

find the value of ∫_0 ^∞ ((cos(ξt))/(1+t^4 ))dt.

$f i n d t h e v a l u e o f \int_{0}^{\infty} \frac{c o s (ξ t)}{1 + t^{4}} d t .$

Question Number 29000 Answers: 0 Comments: 1

prove thst ∫_R (e^(iξx) /(1+x^2 ))dx= π e^(−∣ξ∣) .

$p r o v e t h s t \int_{R} \frac{e^{i ξ x}}{1 + x^{2}} d x = π e^{- ∣ ξ ∣} .$

Question Number 28999 Answers: 0 Comments: 1

prove that ∫_0 ^∞ (e^(−t) /(√t))dt= e^(i(π/4)) ∫_0 ^∞ (e^(−ix) /(√x))dx.

$p r o v e t h a t \int_{0}^{\infty} \frac{e^{- t}}{\sqrt{t}} d t = e^{i \frac{π}{4}} \int_{0}^{\infty} \frac{e^{- i x}}{\sqrt{x}} d x .$

Question Number 28998 Answers: 0 Comments: 0

find ∫_γ (e^z /(z(z+1)))dz with γ={z∈C/ ∣z−1∣=2}

$f i n d \int_{γ} \frac{e^{z}}{z (z + 1)} d z w i t h γ = {z \in C / ∣ z - 1 ∣= 2}$

Question Number 28997 Answers: 0 Comments: 1

find ∫_(−∞) ^(+∞) (dx/((1+x^2 )( 2+e^(ix) ))) .

$f i n d \int_{- \infty}^{+ \infty} \frac{d x}{(1 + x^{2}) (2 + e^{i x})} .$

Question Number 28996 Answers: 0 Comments: 0

find ∫_(−∞) ^(+∞) (x^2 /((x^2 +1)^2 (x^2 +2x+2)))dx.

$f i n d \int_{- \infty}^{+ \infty} \frac{x^{2}}{{(x^{2} + 1)}^{2} (x^{2} + 2 x + 2)} d x .$

Question Number 28995 Answers: 0 Comments: 0

find ∫_0 ^(2π) ((cos(2t))/(3−cost)) dt.

$f i n d \int_{0}^{2 π} \frac{c o s (2 t)}{3 - c o s t} d t .$

Question Number 28994 Answers: 0 Comments: 0

find A_n = ∫_(−∞) ^(+∞) (dx/((1+x^2 )^n )) with n from N and n≥1.

$f i n d A_{n} = \int_{- \infty}^{+ \infty} \frac{d x}{{(1 + x^{2})}^{n}} w i t h n f r o m N a n d n ⩾ 1 .$

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