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IntegrationQuestion and Answers: Page 276

Question Number 39034 Answers: 0 Comments: 1

calculate interms of n A_n = ∫_0 ^(2π) ((cos(nx))/(cosx +sinx))dx and B_n = ∫_0 ^(2π) ((sin(nx))/(cosx +sinx))dx .

$c a l c u l a t e i n t e r m s o f n$ $A_{n} = \int_{0}^{2 π} \frac{c o s (n x)}{c o s x + s i n x} d x a n d B_{n} = \int_{0}^{2 π} \frac{s i n (n x)}{c o s x + s i n x} d x .$

Question Number 39033 Answers: 0 Comments: 2

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

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

Question Number 39025 Answers: 0 Comments: 1

let f(x)= ((cos(αx))/(cosx)) (2π periodic even) developp f at fourier serie.

$l e t f (x) = \frac{c o s (α x)}{c o s x} (2 π p e r i o d i c e v e n)$ $d e v e l o p p f a t f o u r i e r s e r i e .$

Question Number 39024 Answers: 0 Comments: 2

find the value of I = ∫_0 ^1 ((arctan(2x))/(√(1+4x^2 ))) dx

$f i n d t h e v a l u e o f I = \int_{0}^{1} \frac{a r c t a n (2 x)}{\sqrt{1 + 4 x^{2}}} d x$

Question Number 39023 Answers: 0 Comments: 1

let g(x)= ∫_(−∞) ^(+∞) ((arctan(x(1+t^2 )))/(1+t^2 ))dt with x>0 find a simple form of g(x) .

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

Question Number 39020 Answers: 1 Comments: 0

calculate ∫_0 ^1 ((ln(1+(√(x^2 +1))))/(√(x^2 +1))) dx

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

Question Number 39019 Answers: 1 Comments: 3

calculate ∫ (dx/((x^2 +1)(x^2 +2)(x^2 +3))) 1) find the value of ∫_0 ^∞ (dx/((x^2 +1)(x^2 +2)(x^2 +3)))

$c a l c u l a t e \int \frac{d x}{(x^{2} + 1) (x^{2} + 2) (x^{2} + 3)}$ $1) f i n d t h e v a l u e o f \int_{0}^{\infty} \frac{d x}{(x^{2} + 1) (x^{2} + 2) (x^{2} + 3)}$

Question Number 39017 Answers: 0 Comments: 1

find ∫ ((−2x+3)/(x^2 ( x^3 +8)))dx 2) calculate ∫_1 ^(+∞) ((−2x+3)/(x^2 (x^3 +8)))dx

$f i n d \int \frac{- 2 x + 3}{x^{2} (x^{3} + 8)} d x$ $2) c a l c u l a t e \int_{1}^{+ \infty} \frac{- 2 x + 3}{x^{2} (x^{3} + 8)} d x$

Question Number 39016 Answers: 0 Comments: 0

calculate ∫_0 ^π ((sin(nx))/(cosx))dx with n from N .

$c a l c u l a t e \int_{0}^{π} \frac{s i n (n x)}{c o s x} d x w i t h n f r o m N .$

Question Number 39015 Answers: 0 Comments: 2

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

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

Question Number 38946 Answers: 0 Comments: 0

find ∫ arcos(2(√(1−x^2 )))dx .

$f i n d \int a r c o s (2 \sqrt{1 - x^{2}}) d x .$

Question Number 38899 Answers: 0 Comments: 4

find ∫_0 ^π ln(2+cost)dt and ∫_0 ^π ln(2−cost)dt

$f i n d \int_{0}^{π} l n (2 + c o s t) d t a n d \int_{0}^{π} l n (2 - c o s t) d t$

Question Number 38897 Answers: 0 Comments: 0

find ∫ ln((√x) +(√(x+1)) +(√(x+2)))dx

$f i n d \int l n (\sqrt{x} + \sqrt{x + 1} + \sqrt{x + 2}) d x$

Question Number 38896 Answers: 1 Comments: 2

let A_n = ∫_0 ^n ((x[x])/(1+x^2 )) dx 1) calculate A_n 2) find lim_(n→+∞) A_n

$l e t A_{n} = \int_{0}^{n} \frac{x [x]}{1 + x^{2}} d x$ $1) c a l c u l a t e A_{n}$ $2) f i n d {l i m}_{n \to + \infty} A_{n}$

Question Number 39030 Answers: 2 Comments: 3

1) let f(x) = ∫_0 ^∞ (dt/(1+x^2 t^4 )) with x >0 find a simple form of f(x) 2) calculate ∫_0 ^(+∞) (dt/(1+t^4 )) 3) calculate ∫_0 ^∞ (dt/(1+3t^4 ))

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

Question Number 38804 Answers: 1 Comments: 3

let A_n = ∫_0 ^n (((−1)^x )/(2[x] +1))dx 1) calculate A_n 2) find lim_(n→+∞) A_n

$l e t A_{n} = \int_{0}^{n} \frac{{(- 1)}^{x}}{2 [x] + 1} d x$ $1) c a l c u l a t e A_{n}$ $2) f i n d {l i m}_{n \to + \infty} A_{n}$

Question Number 39029 Answers: 2 Comments: 0

∫((3−5(√(1−(1/x)))))^(1/3) dx=? ∫(1/((3−5(√(1−(1/x)))))^(1/3) )dx=?

$\int \sqrt[3]{3 - 5 \sqrt{1 - \frac{1}{x}}} d x = ?$ $\int \frac{1}{\sqrt[3]{3 - 5 \sqrt{1 - \frac{1}{x}}}} d x = ?$

Question Number 38746 Answers: 0 Comments: 3

this is still waiting to be solved... ∫((√((t−1)t(t+1)))/(3t^2 −4))dt=?

$this is still waiting to be solved . . .$ $\int \frac{\sqrt{(t - 1) t (t + 1)}}{3 t^{2} - 4} d t = ?$

Question Number 38728 Answers: 0 Comments: 1

find L ( (e^(−(x/a)) /a)) with a≠0 and L laplace transfom.

$f i n d L (\frac{e^{- \frac{x}{a}}}{a}) w i t h a \neq 0 a n d L l a p l a c e t r a n s f o m .$

Question Number 38727 Answers: 0 Comments: 2

let n from N and A_n = ∫_(−∞) ^(+∞) ((cos(ax))/((x^2 +x+1)^n ))dx and B_n = ∫_(−∞) ^(+∞) ((sin(ax))/((x^2 +x+1)^n ))dx find the value of A_(n ) and B_n .

$l e t n f r o m N a n d A_{n} = \int_{- \infty}^{+ \infty} \frac{c o s (a x)}{{(x^{2} + x + 1)}^{n}} d x a n d$ $B_{n} = \int_{- \infty}^{+ \infty} \frac{s i n (a x)}{{(x^{2} + x + 1)}^{n}} d x$ $f i n d t h e v a l u e o f A_{n} a n d B_{n} .$

Question Number 38724 Answers: 0 Comments: 2

calculate ∫_0 ^∞ ((x^2 cos(πx))/((x^2 +4)^2 ))dx

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

Question Number 38718 Answers: 0 Comments: 3

1) find f(x)=∫_0 ^π ln(2+x cosθ)dθ 2) calculate ∫_0 ^π ln(2 +cosθ)dθ

$1) f i n d f (x) = \int_{0}^{π} l n (2 + x c o s θ) d θ$ $2) c a l c u l a t e \int_{0}^{π} l n (2 + c o s θ) d θ$

Question Number 38720 Answers: 0 Comments: 2

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

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

Question Number 38719 Answers: 1 Comments: 0

find ∫ ln((√x) +(√(x+1)))dx

$f i n d \int l n (\sqrt{x} + \sqrt{x + 1}) d x$

Question Number 38716 Answers: 1 Comments: 1

calculate ∫_2 ^5 (dx/((x +1−[x])^2 ))

$c a l c u l a t e \int_{2}^{5} \frac{d x}{{(x + 1 - [x])}^{2}}$

Question Number 38714 Answers: 1 Comments: 1

calculate ∫_1 ^6 (((−1)^([x]) )/(1+x^2 [x]))dx

$c a l c u l a t e \int_{1}^{6} \frac{{(- 1)}^{[x]}}{1 + x^{2} [x]} d x$

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