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IntegrationQuestion and Answers: Page 295

Question Number 34286 Answers: 0 Comments: 2

find ∫ ((artanx)/((1+x)^2 ))dx

$f i n d \int \frac{a r t a n x}{{(1 + x)}^{2}} d x$

Question Number 34285 Answers: 0 Comments: 3

find ∫ (dx/((1+chx)^2 )) 2) calculate ∫_0 ^1 (dx/((1+chx)^2 ))

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

Question Number 34284 Answers: 0 Comments: 1

find ∫ (dt/(sin(2t)))

$f i n d \int \frac{d t}{s i n (2 t)}$

Question Number 34283 Answers: 0 Comments: 2

calculate ∫_0 ^(π/2) (dx/(cos^4 x +sin^4 x))

$c a l c u l a t e \int_{0}^{\frac{π}{2}} \frac{d x}{{c o s}^{4} x + {s i n}^{4} x}$

Question Number 34282 Answers: 0 Comments: 1

find ∫_(π/6) ^(π/3) (dx/(cos(x) sin(x)))

$f i n d \int_{\frac{π}{6}}^{\frac{π}{3}} \frac{d x}{c o s (x) s i n (x)}$

Question Number 34281 Answers: 0 Comments: 0

calculate ∫_1 ^(√3) ((x−1)/(x^2 (x^2 +1)))dx

$c a l c u l a t e \int_{1}^{\sqrt{3}} \frac{x - 1}{x^{2} (x^{2} + 1)} d x$

Question Number 34280 Answers: 0 Comments: 0

find ∫ ((ln(x+x^2 ))/x^2 )dx

$f i n d \int \frac{l n (x + x^{2})}{x^{2}} d x$

Question Number 34279 Answers: 0 Comments: 0

find ∫_1 ^(+∞) (((−1)^([x]) )/x) dx .

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

Question Number 34278 Answers: 0 Comments: 0

find the value of ∫_0 ^∞ (2 +(t+3)ln(((t+2)/(t+4))))dt .

$f i n d t h e v a l u e o f \int_{0}^{\infty} (2 + (t + 3) l n (\frac{t + 2}{t + 4})) d t .$

Question Number 34277 Answers: 0 Comments: 1

calculate A_n =∫_0 ^∞ (dx/((x+1)(x+2)....(x+n))) n integr≥2 .

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

Question Number 34276 Answers: 0 Comments: 0

nature of ∫_0 ^∞ (dx/(1+x^3 sin^2 x)) ?

$n a t u r e o f \int_{0}^{\infty} \frac{d x}{1 + x^{3} {s i n}^{2} x} ?$

Question Number 34274 Answers: 0 Comments: 0

calculate ∫_2 ^(+∞) ((4x)/(x^4 −1))dx .

$c a l c u l a t e \int_{2}^{+ \infty} \frac{4 x}{x^{4} - 1} d x .$

Question Number 34273 Answers: 0 Comments: 0

calculate ∫_0 ^∞ (e^(arctanx) /(1+x^2 ))dx .

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

Question Number 34271 Answers: 0 Comments: 0

find lim_(n→+∞) ∫_0 ^∞ ((arctan(nx))/(n(1+x^2 )))dx

$f i n d {l i m}_{n \to + \infty} \int_{0}^{\infty} \frac{a r c t a n (n x)}{n (1 + x^{2})} d x$

Question Number 34270 Answers: 0 Comments: 0

let give A_n = ∫_0 ^∞ (dx/((1+x^3 )^n )) 1) calculate A_1 2) for n≥2 find a relation between A_(n+1) and A_n 3) find the value of A_n .

$l e t g i v e A_{n} = \int_{0}^{\infty} \frac{d x}{{(1 + x^{3})}^{n}}$ $1) c a l c u l a t e A_{1}$ $2) f o r n ⩾ 2 f i n d a r e l a t i o n b e t w e e n A_{n + 1} a n d A_{n}$ $3) f i n d t h e v a l u e o f A_{n} .$

Question Number 34269 Answers: 0 Comments: 0

calculate I(λ) =∫_0 ^∞ (dx/((1+x^2 )(1+x^λ )))

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

Question Number 34268 Answers: 0 Comments: 0

calculate I = ∫_(−(π/2)) ^(π/2) ln(1+sinx)dx

$c a l c u l a t e I = \int_{- \frac{π}{2}}^{\frac{π}{2}} l n (1 + s i n x) d x$

Question Number 34266 Answers: 0 Comments: 0

1) find the relation between ∫_x ^(+∞) e^(−t^2 ) dt and ∫_x ^(+∞) (e^(−t^2 ) /t^2 )dt 2) guive a equivalent to ∫_x ^(+∞) e^(−t^2 ) dt when x→+∞

$1) f i n d t h e r e l a t i o n b e t w e e n \int_{x}^{+ \infty} e^{- t^{2}} d t a n d$ $\int_{x}^{+ \infty} \frac{e^{- t^{2}}}{t^{2}} d t$ $2) g u i v e a e q u i v a l e n t t o \int_{x}^{+ \infty} e^{- t^{2}} d t w h e n x \to + \infty$

Question Number 34265 Answers: 0 Comments: 0

find the value of ∫_0 ^∞ e^(−2t) sin([t]) dt .

$f i n d t h e v a l u e o f \int_{0}^{\infty} e^{- 2 t} s i n ([t]) d t .$

Question Number 34264 Answers: 0 Comments: 0

find the value of ∫_0 ^∞ e^(−2[t]) sint dt

$f i n d t h e v a l u e o f \int_{0}^{\infty} e^{- 2 [t]} s i n t d t$

Question Number 34262 Answers: 0 Comments: 0

find the nature of ∫_2 ^(+∞) ((√(1+t^2 +t^4 )) −t ^3 (√(t^3 +at)))dt a∈R .

$f i n d t h e n a t u r e o f \int_{2}^{+ \infty} (\sqrt{1 + t^{2} + t^{4}} - t^{3} \sqrt{t^{3} + a t}) d t$ $a \in R .$

Question Number 34261 Answers: 0 Comments: 0

study the convergence of ∫_0 ^∞ ((t−sint)/t^a )dt with a real.

$s t u d y t h e c o n v e r g e n c e o f \int_{0}^{\infty} \frac{t - s i n t}{t^{a}} d t w i t h a r e a l .$

Question Number 34260 Answers: 0 Comments: 0

let give a>0 1) find the value of F(a) = ∫_0 ^∞ ((lnt)/(t^2 +a^2 ))dt 2) find the value of G(a)=∫_0 ^∞ ((aln(t))/((t^2 +a^2 )^2 ))dt 3) find the value of ∫_0 ^∞ ((ln(t))/((t^2 +3)^2 ))dt

$l e t g i v e a > 0$ $1) f i n d t h e v a l u e o f F (a) = \int_{0}^{\infty} \frac{l n t}{t^{2} + a^{2}} d t$ $2) f i n d t h e v a l u e o f G (a) = \int_{0}^{\infty} \frac{a l n (t)}{{(t^{2} + a^{2})}^{2}} d t$ $3) f i n d t h e v a l u e o f \int_{0}^{\infty} \frac{l n (t)}{{(t^{2} + 3)}^{2}} d t$

Question Number 34257 Answers: 0 Comments: 0

find f(x)= ∫_1 ^x (dt/(t(√(1+t^2 )))) 2) calculate I =∫_1 ^(+∞) (dt/(t(√(1+t^2 ))))

$f i n d f (x) = \int_{1}^{x} \frac{d t}{t \sqrt{1 + t^{2}}}$ $2) c a l c u l a t e I = \int_{1}^{+ \infty} \frac{d t}{t \sqrt{1 + t^{2}}}$

Question Number 34255 Answers: 0 Comments: 0

find g(x)= ∫_0 ^∞ ((ln(1+xt^2 ))/t^2 ) dt 2) calculate ∫_0 ^∞ ((ln(1+3t^2 ))/t^2 )dt .

$f i n d g (x) = \int_{0}^{\infty} \frac{l n (1 + {x t}^{2})}{t^{2}} d t$ $2) c a l c u l a t e \int_{0}^{\infty} \frac{l n (1 + 3 t^{2})}{t^{2}} d t .$

Question Number 34254 Answers: 0 Comments: 0

find I(x)= ∫_0 ^1 ((ln(1+xt^2 ))/t^2 )dt .

$f i n d I (x) = \int_{0}^{1} \frac{l n (1 + {x t}^{2})}{t^{2}} d t .$

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