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Question Number 152617 Answers: 0 Comments: 1

Question Number 152608 Answers: 2 Comments: 0

By using the substitution x=cos 2θ, prove that ∫ (√((1+x)/(1−x))) dx = −sin 2θ−2θ+C

$$\mathrm{By}\:\mathrm{using}\:\mathrm{the}\:\mathrm{substitution}\:{x}=\mathrm{cos}\:\mathrm{2}\theta, \\ $$$$\mathrm{prove}\:\mathrm{that}\:\int\:\sqrt{\frac{\mathrm{1}+{x}}{\mathrm{1}−{x}}}\:{dx}\:=\:−\mathrm{sin}\:\mathrm{2}\theta−\mathrm{2}\theta+{C} \\ $$

Question Number 152588 Answers: 3 Comments: 0

∫_(−1 ) ^1 ((3x+4)/(3+4x+3x^2 ))dt please,help me

$$\int_{−\mathrm{1}\:} ^{\mathrm{1}} \frac{\mathrm{3}{x}+\mathrm{4}}{\mathrm{3}+\mathrm{4}{x}+\mathrm{3}{x}^{\mathrm{2}} }{dt} \\ $$$${please},{help}\:{me} \\ $$

Question Number 152580 Answers: 1 Comments: 0

Question Number 152576 Answers: 0 Comments: 1

∫ ((t + 13)/( ((t^2 + 5t + 6))^(1/3) )) dt

$$\int\:\frac{\mathrm{t}\:\:\:+\:\:\:\mathrm{13}}{\:\sqrt[{\mathrm{3}}]{\mathrm{t}^{\mathrm{2}} \:\:\:+\:\:\:\mathrm{5t}\:\:\:+\:\:\:\mathrm{6}}}\:\:\mathrm{dt} \\ $$

Question Number 152572 Answers: 1 Comments: 0

∫_(−(Π/2)) ^(Π/2) ((1+cosx)/(3+2sinx))dx please,help me

$$\int_{−\frac{\Pi}{\mathrm{2}}} ^{\frac{\Pi}{\mathrm{2}}} \frac{\mathrm{1}+{cosx}}{\mathrm{3}+\mathrm{2}{sinx}}{dx} \\ $$$${please},{help}\:{me} \\ $$

Question Number 152571 Answers: 1 Comments: 0

2log4^x +9logx^4 =9 find x

$$\:\mathrm{2}\boldsymbol{{log}}\mathrm{4}^{\boldsymbol{{x}}} +\mathrm{9}\boldsymbol{{logx}}^{\mathrm{4}} =\mathrm{9} \\ $$$$\boldsymbol{{find}}\:\boldsymbol{{x}} \\ $$

Question Number 152620 Answers: 1 Comments: 1

Question Number 152555 Answers: 2 Comments: 0

𝚺_(k=1) ^n k^5 =?

$$\underset{\boldsymbol{{k}}=\mathrm{1}} {\overset{\boldsymbol{{n}}} {\boldsymbol{\sum}}{k}}^{\mathrm{5}} =? \\ $$

Question Number 152551 Answers: 1 Comments: 0

((sin(x)+sin(2x)+....+sin(nx))/(cos(x)+cos(2x)+....+cos(nx))) = ?

$$\frac{{sin}\left({x}\right)+{sin}\left(\mathrm{2}{x}\right)+....+{sin}\left({nx}\right)}{{cos}\left({x}\right)+{cos}\left(\mathrm{2}{x}\right)+....+{cos}\left({nx}\right)}\:=\:? \\ $$

Question Number 152546 Answers: 1 Comments: 0

Question Number 152545 Answers: 1 Comments: 0

Question Number 152536 Answers: 1 Comments: 2

How many zeroes are there in 99!

$$\mathrm{How}\:\mathrm{many}\:\mathrm{zeroes}\:\mathrm{are}\:\mathrm{there}\:\mathrm{in}\:\:\:\mathrm{99}! \\ $$

Question Number 152533 Answers: 1 Comments: 0

Question Number 152532 Answers: 1 Comments: 0

Question Number 152522 Answers: 1 Comments: 2

Question Number 152791 Answers: 1 Comments: 0

Question Number 152513 Answers: 1 Comments: 1

∫ (1/(2x^2 +3x+8)) dx =?

$$\int\:\frac{\mathrm{1}}{\mathrm{2}{x}^{\mathrm{2}} +\mathrm{3}{x}+\mathrm{8}}\:{dx}\:=? \\ $$

Question Number 152502 Answers: 1 Comments: 0

∫ 9x^2 (4x^2 + 3)^(10) dx

$$\int\:\mathrm{9x}^{\mathrm{2}} \left(\mathrm{4x}^{\mathrm{2}} \:\:+\:\:\mathrm{3}\right)^{\mathrm{10}} \:\mathrm{dx} \\ $$

Question Number 152500 Answers: 0 Comments: 0

Question Number 152498 Answers: 0 Comments: 3

if ((√5) + 2)^6 < x find min(x) = ?

$$\mathrm{if}\:\:\left(\sqrt{\mathrm{5}}\:+\:\mathrm{2}\right)^{\mathrm{6}} \:<\:\mathrm{x} \\ $$$$\mathrm{find}\:\:\mathrm{min}\left(\mathrm{x}\right)\:=\:? \\ $$

Question Number 152496 Answers: 1 Comments: 0

Question Number 152494 Answers: 1 Comments: 0

prove that :: Ω := ∫_(0 ) ^( ∞) (( e^( −x) .ln ((( 1)/( x)) ) sin ( x ))/(x )) dx = (( π)/( 8)) ( 2 γ +ln (2 ) ) ...■ m.n

$$ \\ $$$$\:\:\:\:{prove}\:{that}\::: \\ $$$$\:\:\:\: \\ $$$$\:\:\:\:\:\:\:\:\:\:\Omega\::=\:\int_{\mathrm{0}\:} ^{\:\infty} \frac{\:\:{e}^{\:−{x}} .\mathrm{ln}\:\left(\frac{\:\mathrm{1}}{\:{x}}\:\right)\:{sin}\:\left(\:{x}\:\right)}{{x}\:}\:{dx}\:=\:\frac{\:\pi}{\:\mathrm{8}}\:\left(\:\mathrm{2}\:\gamma\:+\mathrm{ln}\:\left(\mathrm{2}\:\right)\:\right)\:...\blacksquare\:\:\:\:\:\:\:\:\:\:\: \\ $$$$\:\:\:\:\:\:{m}.{n} \\ $$$$ \\ $$

Question Number 152543 Answers: 2 Comments: 0

Solve the equation x^3 −3x=(√(x+2))

$$\:\:\mathrm{Solve}\:\mathrm{the}\:\mathrm{equation}\: \\ $$$$\:\mathrm{x}^{\mathrm{3}} −\mathrm{3x}=\sqrt{\mathrm{x}+\mathrm{2}} \\ $$

Question Number 152486 Answers: 1 Comments: 0

Question Number 152544 Answers: 2 Comments: 1

Find the real zeros of the polynomial P_a (x)=(x^2 +1)(x−1)^2 −ax^2 where a is a given real number

$$\:\mathrm{Find}\:\mathrm{the}\:\mathrm{real}\:\mathrm{zeros}\:\mathrm{of}\:\mathrm{the}\:\mathrm{polynomial} \\ $$$$\:\mathrm{P}_{\mathrm{a}} \left(\mathrm{x}\right)=\left(\mathrm{x}^{\mathrm{2}} +\mathrm{1}\right)\left(\mathrm{x}−\mathrm{1}\right)^{\mathrm{2}} −\mathrm{ax}^{\mathrm{2}} \\ $$$$\mathrm{where}\:\mathrm{a}\:\mathrm{is}\:\mathrm{a}\:\mathrm{given}\:\mathrm{real}\:\mathrm{number} \\ $$

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