Question and Answers Forum

prove the following integral ∫_0 ^(π/2) (x^2 /(sinx))dx=2πG−(7/2)ζ(3) ∫_0 ^1 ln[((x+(√(1−x^2 )))/(x−(√(1−x^2 ))))]^2 (x/(1−x^2 ))dx=((.π^2 )/2) ∫_0 ^∞ ((e^x lnx)/(1+e^(2x) ))dx=(π/2)ln[((Γ((3/4)))/(Γ((1/4))))(√(2π))]

$p r o v e t h e f o l l o w i n g i n t e g r a l$ $\int_{0}^{\frac{π}{2}} \frac{x^{2}}{\sin x} d x = 2 π G - \frac{7}{2} ζ (3)$ $\int_{0}^{1} \ln {[\frac{x + \sqrt{1 - x^{2}}}{x - \sqrt{1 - x^{2}}}]}^{2} \frac{x}{1 - x^{2}} d x = \frac{. π^{2}}{2}$ $\int_{0}^{\infty} \frac{e^{x} \ln x}{1 + e^{2 x}} d x = \frac{π}{2} \ln [\frac{Γ (\frac{3}{4})}{Γ (\frac{1}{4})} \sqrt{2 π}]$

Question Number 113587 Answers: 2 Comments: 1

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 113578 Answers: 1 Comments: 2

Question Number 113576 Answers: 1 Comments: 0

lim_(r→∞) (√(4r^2 +2r)) −((8r^3 +4r^2 ))^(1/(3 )) =?

$\lim_{r \to \infty} \sqrt{4 r^{2} + 2 r} - \sqrt[3]{8 r^{3} + 4 r^{2}} = ?$

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 113554 Answers: 2 Comments: 0

Using displacement vector (((−4)),((−2)) ), what is the image of ((6),(3) ) when translated?

$Using displacement vector (\begin{matrix} - 4 \\ - 2 \end{matrix}),$ $what is the image of (\begin{matrix} 6 \\ 3 \end{matrix}) when$ $translated ?$

Question Number 113552 Answers: 1 Comments: 0

Question Number 113549 Answers: 0 Comments: 0

let A = (((1 −(1/n))),(((1/n) 1)) ) 1) calculate A^2 2) calculate A^m (m integr natural) 3) coclude A^n and lim_(n→+∞) A^n 4) calculate e^A and e^(−A)

$let A = (\begin{matrix} 1 - \frac{1}{n} \\ \frac{1}{n} 1 \end{matrix})$ $1) calculate A^{2}$ $2) calculate A^{m} (m integr natural)$ $3) coclude A^{n} and \lim_{n \to + \infty} A^{n}$ $4) calculate e^{A} and e^{- A}$

Question Number 113542 Answers: 0 Comments: 2

App Update v2.203 A function plotter for one variable is available. Steps to use Insert Drawing Insert Equation select equation from the list of shape tap on BUILD and select plot A sample plot is show as image below. Line color for plot can be changed using edit shape menu to change range of x values select scale from options menu. to zoomin/out use option menu to scroll with zoom: clear selection and place touch in move mode. You can add multiple plots on one drawing and also add another drawing on the canvas.

$App Update v 2 . 203$ $A function plotter for one variable$ $is available . Steps to use$ $Insert Drawing$ $Insert Equation$ $select equation from the list of shape$ $tap on BUILD and select plot$ $A sample plot is show as image below .$ $Line color for plot can be changed$ $using edit shape menu$ $to change range of x values select$ $scale from options menu .$ $to zoomin / out use option menu$ $to scroll with zoom : clear selection and$ $place touch in move mode .$ $You can add multiple plots on$ $one drawing and also add another$ $drawing on the canvas .$

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