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IntegrationQuestion and Answers: Page 136

Question Number 113867 Answers: 1 Comments: 0

∫_3 ^6 ((x+1)/(x^3 +x^2 −6x))dx

$\int_{3}^{6} \frac{x + 1}{x^{3} + x^{2} - 6 x} dx$

Question Number 113865 Answers: 0 Comments: 0

Consider the series I_n =∫_1 ^e x(lnx)^n dx and I_0 =∫_1 ^e xdx Which of the following is true ? a\ 0≤I_n ≤(e^2 /(n+2)) b\1≤I_n ≤(e^2 /(n+1)) c\I_n is negative

$Consider the series I_{n} = \int_{1}^{e} x {(lnx)}^{n} dx and I_{0} = \int_{1}^{e} xdx$ $Which of the following is true ?$ $a ∖ 0 ⩽ I_{n} ⩽ \frac{e^{2}}{n + 2} b ∖ 1 ⩽ I_{n} ⩽ \frac{e^{2}}{n + 1} c ∖ I_{n} is negative$

Question Number 113821 Answers: 3 Comments: 1

∫_0 ^(π/2) ln(2−sinx)dx

$\int_{0}^{\frac{π}{2}} \ln (2 - sinx) dx$

Question Number 113766 Answers: 1 Comments: 0

I=∫_0 ^∞ ((π/(1+π^2 x^2 ))−(1/(1+x^2 )))lnx dx put πx=tanA, x =tanB I=∫_0 ^(π/2) (ln(tanA)−lnπ)dA−∫_0 ^(π/2) ln(tanB)dB I=((−π)/2)lnπ

$I = \int_{0}^{\infty} (\frac{π}{1 + π^{2} x^{2}} - \frac{1}{1 + x^{2}}) l n x d x$ $p u t π x = t a n A, x = t a n B$ $I = \int_{0}^{\frac{π}{2}} (l n (t a n A) - l n π) d A - \int_{0}^{π / 2} l n (t a n B) d B$ $I = \frac{- π}{2} l n π$

Question Number 113760 Answers: 1 Comments: 0

∫(√((x−1)/x^5 ))dx

$\int \sqrt{\frac{x - 1}{x^{5}}} dx$

Question Number 113745 Answers: 1 Comments: 0

Question Number 113738 Answers: 1 Comments: 0

∫_0 ^π ((x sin x)/(1+cos^2 x)) dx ?

$\underset{0}{\int^{π}} \frac{x \sin x}{1 + \cos^{2} x} d x ?$

Question Number 113757 Answers: 2 Comments: 0

∫ (dx/(tan x−sin x)) ?

$\int \frac{d x}{\tan x - \sin x} ?$

Question Number 113675 Answers: 1 Comments: 3

Question Number 113656 Answers: 1 Comments: 0

∫ (((1+tan (((3x)/2)))^2 )/(1+sin 3x)) dx ?

$\int \frac{{(1 + \tan (\frac{3 x}{2}))}^{2}}{1 + \sin 3 x} dx ?$

Question Number 113634 Answers: 2 Comments: 0

Bonjour besoin d′aide Calculer ∫ln(cosx)dx

$B o n j o u r b e s o i n d^{'} a i d e$ $C a l c u l e r \int l n (c o s x) d x$

Question Number 113630 Answers: 3 Comments: 0

explicit g(a) =∫_0 ^(π/4) ln(1+acos^2 θ)dθ

$explicit g (a) = \int_{0}^{\frac{π}{4}} \ln (1 + {acos}^{2} θ) d θ$

Question Number 113629 Answers: 0 Comments: 0

find f(a) =∫_0 ^(π/8) ln(1+a sinθ)dθ with o<a<1

$find f (a) = \int_{0}^{\frac{π}{8}} \ln (1 + a \sin θ) d θ with o < a < 1$

Question Number 113600 Answers: 1 Comments: 0

Prouver que β(a,b)=((Γ(a)Γ(b))/(Γ(a+b)))=∫_0 ^1 x^(a−1) (1−x)^(b−1) dx

$P r o u v e r q u e$ $β (a, b) = \frac{Γ (a) Γ (b)}{Γ (a + b)} = \int_{0}^{1} x^{a - 1} {(1 - x)}^{b - 1} d x$

Question Number 113628 Answers: 1 Comments: 0

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

$find \int \frac{dx}{(x + 1) \sqrt{x^{2} - 1} + (x - 1) \sqrt{x^{2} + 1}}$

Question Number 113627 Answers: 0 Comments: 0

calculate ∫_0 ^∞ (dx/(x^4 +ix^2 +2))

$calculate \int_{0}^{\infty} \frac{dx}{x^{4} + {ix}^{2} + 2}$

Question Number 113565 Answers: 1 Comments: 0

Question Number 113564 Answers: 1 Comments: 0

∫_1 ^2 f(2x+1) dx = 3 and ∫_1 ^2 (x^2 f(x^3 +2))dx = 5 then ∫_5 ^(10) f(x) dx = ?

$\int_{1}^{2} f (2 x + 1) d x = 3 a n d$ $\int_{1}^{2} (x^{2} f (x^{3} + 2)) d x = 5$ $t h e n \int_{5}^{10} f (x) d x = ?$

Question Number 113562 Answers: 1 Comments: 0

calculate ∫_0 ^∞ (dx/(x^4 +ix^2 +2))

$calculate \int_{0}^{\infty} \frac{dx}{x^{4} + {ix}^{2} + 2}$

Question Number 113421 Answers: 0 Comments: 2

Question Number 113418 Answers: 3 Comments: 1

∫ ((3x−2)/( (√(x^2 +2x+26)))) dx

$\int \frac{3 x - 2}{\sqrt{x^{2} + 2 x + 26}} dx$

Question Number 113323 Answers: 2 Comments: 0

Question Number 113275 Answers: 2 Comments: 0

∫ (dx/(3sin x+sin^3 x)) ?

$\int \frac{dx}{3 \sin x + \sin^{3} x} ?$

Question Number 113218 Answers: 1 Comments: 0

Question Number 113203 Answers: 1 Comments: 0

calculate ∫_0 ^∞ (dx/(x^4 +2x^2 +3))

$c a l c u l a t e \int_{0}^{\infty} \frac{d x}{x^{4} + 2 x^{2} + 3}$

Question Number 113198 Answers: 1 Comments: 0

.... calculus.... Evaluate ::: I :=∫_0 ^( 1) (1/( (√(x(x+1)(x+2)(x+3)+1))−3x))dx=??? M.N.july 1970#

$. . . . c a l c u l u s . . . .$ $E v a l u a t e :::$ $I := \int_{0}^{1} \frac{1}{\sqrt{x (x + 1) (x + 2) (x + 3) + 1} - 3 x} d x = ? ? ?$ $You can't use 'macro parameter character #' in math mode$

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