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Question Number 81851    Answers: 0   Comments: 0

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

$$\left.\mathrm{1}\right){find}\:\int\:\:\:\:\frac{{dx}}{\left({x}+\mathrm{1}\right)^{\mathrm{3}} \left({x}^{\mathrm{2}} +\mathrm{1}\right)^{\mathrm{2}} } \\ $$$$\left.\mathrm{2}\right)\:{calculate}\:\int_{\mathrm{0}} ^{\infty} \:\:\:\frac{{dx}}{\left({x}+\mathrm{1}\right)^{\mathrm{3}} \left({x}^{\mathrm{2}} +\mathrm{1}\right)^{\mathrm{2}} } \\ $$

Question Number 81836    Answers: 0   Comments: 0

Question Number 81835    Answers: 0   Comments: 1

Question Number 81829    Answers: 1   Comments: 2

Question Number 81828    Answers: 0   Comments: 0

Question Number 81824    Answers: 1   Comments: 0

Question Number 81821    Answers: 1   Comments: 0

Question Number 81804    Answers: 2   Comments: 1

Question Number 81801    Answers: 1   Comments: 1

Question Number 81797    Answers: 0   Comments: 1

Question Number 81794    Answers: 1   Comments: 2

Question Number 81786    Answers: 0   Comments: 5

Question Number 81913    Answers: 0   Comments: 1

Question Number 81771    Answers: 1   Comments: 3

Question Number 81769    Answers: 0   Comments: 2

Question Number 81768    Answers: 1   Comments: 4

Question Number 81763    Answers: 0   Comments: 2

Q. Find the minimum value of 3cosx + 4sinx + 8.

$${Q}.\:{Find}\:{the}\:{minimum}\:{value}\:{of}\: \\ $$$$\mathrm{3}{cosx}\:+\:\mathrm{4}{sinx}\:+\:\mathrm{8}. \\ $$

Question Number 81760    Answers: 0   Comments: 2

prove sin a+sin b+sin c =? 4cos ((a/2))cos ((b/2))cos ((c/2))

$${prove}\: \\ $$$$\mathrm{sin}\:{a}+\mathrm{sin}\:{b}+\mathrm{sin}\:{c}\:=? \\ $$$$\mathrm{4cos}\:\left(\frac{{a}}{\mathrm{2}}\right)\mathrm{cos}\:\left(\frac{{b}}{\mathrm{2}}\right)\mathrm{cos}\:\left(\frac{{c}}{\mathrm{2}}\right) \\ $$

Question Number 81759    Answers: 0   Comments: 1

Question Number 81755    Answers: 1   Comments: 0

Question Number 81750    Answers: 0   Comments: 0

Question Number 81741    Answers: 0   Comments: 2

Question Number 81740    Answers: 0   Comments: 1

Question Number 81739    Answers: 2   Comments: 1

∫(dx/(cos^3 x−sin^3 x))

$$\int\frac{{dx}}{{cos}^{\mathrm{3}} {x}−{sin}^{\mathrm{3}} {x}} \\ $$

Question Number 81734    Answers: 0   Comments: 4

The vertices of quadrilateral lie on the graph of y = lnx and the x−coordinates of these vertices are consecutive positive integer . The area of the quadrilateral is ln (((91)/(90))). what is the x−coordinate of the leftmost vertex

$${The}\:{vertices}\:{of}\:{quadrilateral} \\ $$$${lie}\:{on}\:{the}\:{graph}\:{of}\:{y}\:=\:{lnx}\:{and}\: \\ $$$${the}\:{x}−{coordinates}\:{of}\:{these}\:{vertices} \\ $$$${are}\:{consecutive}\:{positive}\:{integer} \\ $$$$.\:{The}\:{area}\:{of}\:{the}\:{quadrilateral} \\ $$$${is}\:{ln}\:\left(\frac{\mathrm{91}}{\mathrm{90}}\right).\:{what}\:{is}\:{the}\:{x}−{coordinate} \\ $$$${of}\:{the}\:{leftmost}\:{vertex} \\ $$

Question Number 81733    Answers: 0   Comments: 2

Σ_(n=1) ^∞ (n/((n+1)∙5^n )) = ?

$$\underset{{n}=\mathrm{1}} {\overset{\infty} {\sum}}\:\frac{{n}}{\left({n}+\mathrm{1}\right)\centerdot\mathrm{5}^{{n}} }\:\:=\:\:? \\ $$

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