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Question Number 151276 Answers: 2 Comments: 2

∫_0 ^(2π) cos^(−1) (cos x)dx

$\int_{0}^{2 π} \cos^{- 1} (\cos x) dx$

Question Number 151272 Answers: 0 Comments: 1

Question Number 151269 Answers: 0 Comments: 1

Question Number 151268 Answers: 0 Comments: 0

Σ_(r=1) ^∞ (((−1)^(r−1) )/r)[ψ((r/2)+(1/4))−ψ((r/2)−(1/4))]

$\underset{r = 1}{\sum^{\infty}} \frac{{(- 1)}^{r - 1}}{r} [ψ (\frac{r}{2} + \frac{1}{4}) - ψ (\frac{r}{2} - \frac{1}{4})]$

Question Number 151265 Answers: 1 Comments: 3

Question Number 151256 Answers: 2 Comments: 0

A_n =2^n +3^n +4^n +5^n B_n =100^n +101^n +102^n +103^n 1)find values of n while 7∣A_n 2) show that B_n ≡A_n [7 ]

$A_{n} = 2^{n} + 3^{n} + 4^{n} + 5^{n}$ $B_{n} = 100^{n} + 101^{n} + 102^{n} + 103^{n}$ $1) f i n d v a l u e s o f n w h i l e 7 ∣ A_{n}$ $2) s h o w t h a t B_{n} \equiv A_{n} [7]$

Question Number 151248 Answers: 1 Comments: 0

Question Number 151247 Answers: 1 Comments: 0

(1/5) + (1/(5^2 ∙2)) + (1/(5^3 ∙3)) + (1/(5^4 ∙4)) + ... = ?

$\frac{1}{5} + \frac{1}{5^{2} \cdot 2} + \frac{1}{5^{3} \cdot 3} + \frac{1}{5^{4} \cdot 4} + . . . = ?$

Question Number 151246 Answers: 1 Comments: 0

find I=∫_0 ^(π/4) ln(cosx)dx and J=∫_0 ^(π/4) ln(sinx)dx

$find I = \int_{0}^{\frac{π}{4}} \ln (cosx) dx and J = \int_{0}^{\frac{π}{4}} \ln (sinx) dx$

Question Number 151241 Answers: 1 Comments: 0

Question Number 151230 Answers: 4 Comments: 2

prove: ∫_0 ^( ∞) (( ln ( 1+x^( 2) ))/(x^( 2) (1+x^( 2) )))dx= π ln((e/2) ) ..

$p r o v e :$ $\int_{0}^{\infty} \frac{l n (1 + x^{2})}{x^{2} (1 + x^{2})} d x = π l n (\frac{e}{2}) . .$

Question Number 151226 Answers: 0 Comments: 0

Question Number 151224 Answers: 1 Comments: 0

Question Number 151221 Answers: 1 Comments: 2

∫((sin x)/(sin (x−a)))dx

$\int \frac{\sin x}{\sin (x - a)} dx$

Question Number 151220 Answers: 3 Comments: 0

show that ∫_0 ^(π/2) ((cos x)/(cos x+sin x+1))dx=(1/4)(π−2ln 2)

$show that$ $\int_{0}^{\frac{π}{2}} \frac{\cos x}{\cos x + \sin x + 1} dx = \frac{1}{4} (π - 2 \ln 2)$

Question Number 151218 Answers: 0 Comments: 2

Question Number 151216 Answers: 1 Comments: 0

Solve for real number ((x+3))^(1/7) +((6−x))^(1/7) = (9)^(1/7)

$Solve for real number$ $\sqrt[7]{x + 3} + \sqrt[7]{6 - x} = \sqrt[7]{9}$

Question Number 151215 Answers: 1 Comments: 0

if x;y;z>0 ; x+y+z=1 and λ≥(1/6) then: 𝛌 Σ ((y + z)/x) + 3 Σ yz ≥ 6𝛌 + 1

$if x; y; z > 0; x + y + z = 1 and λ ⩾ \frac{1}{6} then :$ $λ Σ \frac{y + z}{x} + 3 Σ yz ⩾ 6 λ + 1$

Question Number 151212 Answers: 1 Comments: 0

if a_1 ,a_2 ,...a_n >1 then: (√(((a_1 -1)(a_2 -1)...(a_n -1))/((a_1 +1)(a_2 +1)...(a_n +1)))) ≤ ((a_1 a_2 ...a_n )/2^n )

$if a_{1}, a_{2}, . . . a_{n} > 1 then :$ $\sqrt{\frac{(a_{1} - 1) (a_{2} - 1) . . . (a_{n} - 1)}{(a_{1} + 1) (a_{2} + 1) . . . (a_{n} + 1)}} ⩽ \frac{a_{1} a_{2} . . . a_{n}}{2^{n}}$

Question Number 151211 Answers: 1 Comments: 0

Find the coefficient of x^9 from expression (1+x)(1+2x^2 )(1+3x^3 )(1+4x^4 )(1+5x^5 )...(1+10x^(10) )

$F i n d t h e c o e f f i c i e n t o f x^{9}$ $f r o m e x p r e s s i o n$ $(1 + x) (1 + 2 x^{2}) (1 + 3 x^{3}) (1 + 4 x^{4}) (1 + 5 x^{5}) . . . (1 + 10 x^{10})$

Question Number 151208 Answers: 0 Comments: 0

Question Number 151204 Answers: 1 Comments: 0

Question Number 151205 Answers: 1 Comments: 0

determinant ((((2+(√3))^x +1 =(2(√(2+(√3))))^x )),((x =? )))

$\underset{⏟}{} \begin{array}{cc} {(2 + \sqrt{3})}^{x} + 1 = {(2 \sqrt{2 + \sqrt{3}})}^{x} \\ x = ? \end{array}$

Question Number 151198 Answers: 1 Comments: 0

If a,b∈R satisfy a^4 +b^4 −6a^2 b^2 =9 and ab(a−b)(a+b)=−11 then a^2 +b^2 =?

$If a, b \in R satisfy a^{4} + b^{4} - 6 a^{2} b^{2} = 9 a n d$ $a b (a - b) (a + b) = - 11 then a^{2} + b^{2} = ?$

Question Number 151193 Answers: 0 Comments: 0

Question Number 151192 Answers: 0 Comments: 1

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