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Question Number 79615 Answers: 0 Comments: 3

prove that with using hypergeometric function ∫_0 ^π sin(x^2 )=(π^3 /3) 1F_2 [(3/4);(3/2);(7/4);((−π^4 )/4)]

$${prove}\:{that}\:{with}\:{using}\:{hypergeometric}\:{function} \\ $$$$\int_{\mathrm{0}} ^{\pi} {sin}\left({x}^{\mathrm{2}} \right)=\frac{\pi^{\mathrm{3}} }{\mathrm{3}}\:\mathrm{1}{F}_{\mathrm{2}} \left[\frac{\mathrm{3}}{\mathrm{4}};\frac{\mathrm{3}}{\mathrm{2}};\frac{\mathrm{7}}{\mathrm{4}};\frac{−\pi^{\mathrm{4}} }{\mathrm{4}}\right]\: \\ $$

Question Number 79609 Answers: 1 Comments: 1

Question Number 79607 Answers: 0 Comments: 1

Solve this ∫_ (((x−yz))/((x^2 +y^2 −2xyz)^(3/2) ))dz

$${Solve}\:{this} \\ $$$$\int_{} \frac{\left({x}−{yz}\right)}{\left({x}^{\mathrm{2}} +{y}^{\mathrm{2}} −\mathrm{2}{xyz}\right)^{\mathrm{3}/\mathrm{2}} }{dz} \\ $$$$ \\ $$$$ \\ $$

Question Number 79588 Answers: 1 Comments: 3

f(x) = (1/(1+2(√(2x))+2x))+(x/4) prove that f(x) ≥ (3/8) .

$${f}\left({x}\right)\:=\:\frac{\mathrm{1}}{\mathrm{1}+\mathrm{2}\sqrt{\mathrm{2}{x}}+\mathrm{2}{x}}+\frac{{x}}{\mathrm{4}} \\ $$$$\mathrm{prove}\:\mathrm{that}\:{f}\left({x}\right)\:\geqslant\:\frac{\mathrm{3}}{\mathrm{8}}\:. \\ $$

Question Number 79580 Answers: 0 Comments: 5

does this matter reasonable ∫ sin^x (x) dx ?

$$\mathrm{does}\:\mathrm{this}\:\mathrm{matter}\:\mathrm{reasonable} \\ $$$$\int\:\mathrm{sin}\:^{\mathrm{x}} \left(\mathrm{x}\right)\:\mathrm{dx}\:? \\ $$

Question Number 79572 Answers: 1 Comments: 1

Question Number 79571 Answers: 1 Comments: 5

Solve for x: ((x + ((x + ((x + ...))^(1/3) ))^(1/3) ))^(1/3) = ((x ((x ((x ....))^(1/3) ))^(1/3) ))^(1/3)

$$\mathrm{Solve}\:\mathrm{for}\:\mathrm{x}: \\ $$$$\:\sqrt[{\mathrm{3}}]{\mathrm{x}\:\:+\:\:\sqrt[{\mathrm{3}}]{\mathrm{x}\:\:+\:\:\sqrt[{\mathrm{3}}]{\mathrm{x}\:\:+\:\:...}}}\:\:\:\:\:\:\:=\:\:\:\:\:\sqrt[{\mathrm{3}}]{\mathrm{x}\:\:\sqrt[{\mathrm{3}}]{\mathrm{x}\:\:\sqrt[{\mathrm{3}}]{\mathrm{x}\:\:....}}} \\ $$

Question Number 79613 Answers: 1 Comments: 0

3xy(2x−y)−3bx+3c=0 3xy(x−2y)−3by−3c=0 find non-zero, real values of x,y if b,c∈R.

$$\mathrm{3}{xy}\left(\mathrm{2}{x}−{y}\right)−\mathrm{3}{bx}+\mathrm{3}{c}=\mathrm{0} \\ $$$$\mathrm{3}{xy}\left({x}−\mathrm{2}{y}\right)−\mathrm{3}{by}−\mathrm{3}{c}=\mathrm{0} \\ $$$${find}\:{non}-{zero},\:{real}\:{values} \\ $$$${of}\:{x},{y}\:\:{if}\:{b},{c}\in\mathbb{R}. \\ $$

Question Number 79612 Answers: 1 Comments: 0

∫ (dx/((√(x ))((x)^(1/(4 )) +1)^(10) )) = ?

$$\int\:\frac{\mathrm{dx}}{\sqrt{\mathrm{x}\:}\left(\sqrt[{\mathrm{4}\:}]{\mathrm{x}}+\mathrm{1}\right)^{\mathrm{10}} }\:=\:? \\ $$

Question Number 79565 Answers: 0 Comments: 2

lim_(x→∞) (x−(√(x^2 −x+1)) )×(((ln(e^x +x))/x))

$$\underset{{x}\rightarrow\infty} {\mathrm{lim}}\left(\mathrm{x}−\sqrt{\mathrm{x}^{\mathrm{2}} −\mathrm{x}+\mathrm{1}}\:\right)×\left(\frac{\mathrm{ln}\left(\mathrm{e}^{\mathrm{x}} +\mathrm{x}\right)}{\mathrm{x}}\right) \\ $$

Question Number 79560 Answers: 0 Comments: 1

(√(1+x)) ≤ ((5−x))^(1/(4 ))

$$\sqrt{\mathrm{1}+\mathrm{x}}\:\leqslant\:\sqrt[{\mathrm{4}\:}]{\mathrm{5}−\mathrm{x}} \\ $$

Question Number 79538 Answers: 1 Comments: 13

Question Number 79536 Answers: 0 Comments: 4

Question Number 79532 Answers: 1 Comments: 2

Given function f : R ⇒ R x^2 f(x) + f(1 − x) = 2x − x^4 f(2019) = ?

$${Given}\:\:{function}\:\:{f}\::\:\mathbb{R}\:\:\Rightarrow\:\:\mathbb{R} \\ $$$$\:\:\:\:\:\:\:\:{x}^{\mathrm{2}} \:{f}\left({x}\right)\:+\:{f}\left(\mathrm{1}\:−\:{x}\right)\:\:=\:\:\mathrm{2}{x}\:−\:{x}^{\mathrm{4}} \\ $$$${f}\left(\mathrm{2019}\right)\:\:=\:\:? \\ $$

Question Number 79531 Answers: 0 Comments: 1

∫^1 _0 ((ln((1/x)+x))/(x^2 +1))dx ?

$$\underset{\mathrm{0}} {\int}^{\mathrm{1}} \:\frac{\mathrm{ln}\left(\frac{\mathrm{1}}{\mathrm{x}}+\mathrm{x}\right)}{\mathrm{x}^{\mathrm{2}} +\mathrm{1}}\mathrm{dx}\:? \\ $$

Question Number 79528 Answers: 0 Comments: 0

find ∫_0 ^∞ e^(−x^3 ) cos(x^2 )dx

$${find}\:\int_{\mathrm{0}} ^{\infty} \:{e}^{−{x}^{\mathrm{3}} } {cos}\left({x}^{\mathrm{2}} \right){dx} \\ $$

Question Number 79527 Answers: 0 Comments: 1

find ∫_0 ^∞ e^(−x^3 ) dx

$${find}\:\int_{\mathrm{0}} ^{\infty} \:{e}^{−{x}^{\mathrm{3}} } {dx} \\ $$

Question Number 79520 Answers: 1 Comments: 2

Question Number 79516 Answers: 0 Comments: 3

Question Number 79515 Answers: 0 Comments: 0

Question Number 79513 Answers: 0 Comments: 1

Q.solve if t^2 =n^2 cos^2 (x)+m^2 sin^2 (x) then show that: t+(d^2 t/dx^2 )=(((nm)^2 )/t^3 )

$${Q}.{solve} \\ $$$${if}\:{t}^{\mathrm{2}} ={n}^{\mathrm{2}} {cos}^{\mathrm{2}} \left({x}\right)+{m}^{\mathrm{2}} {sin}^{\mathrm{2}} \left({x}\right) \\ $$$$ \\ $$$${then}\:{show}\:{that}: \\ $$$${t}+\frac{{d}^{\mathrm{2}} {t}}{{dx}^{\mathrm{2}} }=\frac{\left({nm}\right)^{\mathrm{2}} }{{t}^{\mathrm{3}} } \\ $$$$ \\ $$

Question Number 79512 Answers: 0 Comments: 0

Q.solve if t^2 =n^2 cos^2 (x)+m^2 sin^2 (x) then show that: t+(d^2 t/dx^2 )=(((nm)^2 )/t^3 )

Question Number 79852 Answers: 2 Comments: 1

Question Number 79500 Answers: 1 Comments: 0

∫(cot^2 x+cot^4 x)dx

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

Question Number 79499 Answers: 0 Comments: 2

∫_0 ^(30π) ∣sin x∣ dx=

$$\underset{\mathrm{0}} {\overset{\mathrm{30}\pi} {\int}}\mid\mathrm{sin}\:\mathrm{x}\mid\:\mathrm{dx}=\: \\ $$

Question Number 79491 Answers: 0 Comments: 4

Find the number of used place

$$\mathrm{Find}\:\mathrm{the}\:\mathrm{number}\:\mathrm{of}\:\mathrm{used}\:\mathrm{place} \\ $$

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