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Question Number 166376 Answers: 0 Comments: 0

Question Number 166378 Answers: 1 Comments: 0

8x^3 −6x+1=0 solve for x

$8 x^{3} - 6 x + 1 = 0$ $s o l v e f o r x$

Question Number 166373 Answers: 0 Comments: 0

prove 𝛗=∫_0 ^( 1) (( ln^( 2) (1−x^( 2) ) )/x^( 2) ) dx =(π^( 2) /3) −4ln^( 2) (2) −−− solution (technical method) −−− 𝛗= ∫_0 ^( 1) ln^( 2) (1−x^( 2) )d(1−(1/x)) = [(1−(1/x))ln^( 2) (1−x^( 2) )]_0 ^1 +4∫_0 ^( 1) (1−(1/x))((xln(1−x^( 2) ))/(1−x^( 2) ))dx = −4∫_0 ^( 1) ((ln(1−x^( 2) ))/(1+x)) dx = −4∫_0 ^( 1) ((ln(1+x))/(1+x))dx −4∫_0 ^( 1) ((ln(1−x)dx)/(1+x)) = −2ln^( 2) (2) −4 ( −(π^( 2) /(12)) +(1/2)ln^( 2) (2)) ∴ 𝛗= (π^( 2) /3) −4ln^( 2) (2) ■ m.n

$p r o v e$ $ϕ = \int_{0}^{1} \frac{{l n}^{2} (1 - x^{2})}{x^{2}} d x = \frac{π^{2}}{3} - 4 {l n}^{2} (2)$ $- - - s o l u t i o n (t e c h n i c a l m e t h o d) - - -$ $ϕ = \int_{0}^{1} {l n}^{2} (1 - x^{2}) d (1 - \frac{1}{x})$ $= {[(1 - \frac{1}{x}) {l n}^{2} (1 - x^{2})]}_{0}^{1} + 4 \int_{0}^{1} (1 - \frac{1}{x}) \frac{x l n (1 - x^{2})}{1 - x^{2}} d x$ $= - 4 \int_{0}^{1} \frac{l n (1 - x^{2})}{1 + x} d x$ $= - 4 \int_{0}^{1} \frac{l n (1 + x)}{1 + x} d x - 4 \int_{0}^{1} \frac{l n (1 - x) d x}{1 + x}$ $= - 2 {l n}^{2} (2) - 4 (- \frac{π^{2}}{12} + \frac{1}{2} {l n}^{2} (2))$ $∴ ϕ = \frac{π^{2}}{3} - 4 {l n}^{2} (2) ◼ m . n$

Question Number 166371 Answers: 0 Comments: 2

Question Number 166372 Answers: 3 Comments: 0

Question Number 166360 Answers: 1 Comments: 0

((sin 10x)/(sin 2x))−((cos 10x)/(cos 2x))=?

$\frac{\sin 10 x}{s i n 2 x} - \frac{\cos 10 x}{\cos 2 x} = ?$

Question Number 166358 Answers: 1 Comments: 0

Question Number 166350 Answers: 1 Comments: 1

Question Number 166331 Answers: 2 Comments: 1

prove that ((df^(−1) (a))/dx)×((df(f^(−1) (a)))/dx)=1

$p r o v e t h a t$ $\frac{{d f}^{- 1} (a)}{d x} \times \frac{d f (f^{- 1} (a))}{d x} = 1$

Question Number 166321 Answers: 1 Comments: 0

Question Number 166320 Answers: 1 Comments: 0

∫ (dx/(tan^2 x+sin^2 x)) =?

$\int \frac{dx}{\tan^{2} x + \sin^{2} x} = ?$

Question Number 166319 Answers: 1 Comments: 2

Question Number 166318 Answers: 0 Comments: 0

Question Number 166346 Answers: 1 Comments: 1

∫(dx/(1+(√x)+(√(1+x))))

$\int \frac{d x}{1 + \sqrt{x} + \sqrt{1 + x}}$

Question Number 166307 Answers: 1 Comments: 0

∫_0 ^1 ((x^4 (1−x)^4 )/(1+x^2 ))dx

$\int_{0}^{1} \frac{x^{4} {(1 - x)}^{4}}{1 + x^{2}} d x$

Question Number 166296 Answers: 0 Comments: 2

(cos x)^(2022) −(sin x)^(2022) =1 x=?

${(\cos x)}^{2022} - {(\sin x)}^{2022} = 1$ $x = ?$

Question Number 166294 Answers: 0 Comments: 5

f(x)=∫_1 ^x (dt/( (√(t^3 +2t^2 +3)))) (f^(−1) (0))′=?

$f (x) = \int_{1}^{x} \frac{d t}{\sqrt{t^{3} + 2 t^{2} + 3}}$ ${(f^{- 1} (0))}^{'} = ?$

Question Number 166291 Answers: 1 Comments: 0

calculer la somme Σ_(n=1) ^(+oo) (1/(n(n+2)))x^n

$c a l c u l e r l a s o m m e$ $\underset{n = 1}{\sum^{+ o o}} \frac{1}{n (n + 2)} x^{n}$

Question Number 166284 Answers: 0 Comments: 1

Question Number 166281 Answers: 1 Comments: 0

Question Number 166280 Answers: 1 Comments: 0

Solve for the exact value of ∫_0 ^( ∞) sin(x^2 + x^(−2) ) dx

$Solve for the exact value of \int_{0}^{\infty} \sin (x^{2} + x^{- 2}) dx$

Question Number 166279 Answers: 0 Comments: 0

if y = x^x^x^x find y^′ ?

$i f y = x^{x^{x^{x}}} f i n d y^{^{'}} ?$

Question Number 166273 Answers: 2 Comments: 1

Question Number 166263 Answers: 1 Comments: 0

∫_( −(π/4)) ^( (π/4)) (dx/(cos^2 x (√(9+7 tan ∣x∣)))) dx =?

$\int_{- \frac{π}{4}}^{\frac{π}{4}} \frac{dx}{\cos^{2} x \sqrt{9 + 7 \tan ∣ x ∣}} dx = ?$

Question Number 166301 Answers: 2 Comments: 0

∫(x/( (√(1+x^2 +(√((1+x^2 )^3 ))))))dx

$\int \frac{x}{\sqrt{1 + x^{2} + \sqrt{{(1 + x^{2})}^{3}}}} d x$

Question Number 166261 Answers: 1 Comments: 1

If four men can dig a piece of land in 2days at eight hours everyday.How many days can two men dig in every six hours perday?

$I f f o u r m e n c a n d i g a p i e c e o f l a n d i n 2 d a y s a t e i g h t h o u r s e v e r y d a y . H o w m a n y d a y s c a n t w o m e n d i g i n e v e r y s i x h o u r s p e r d a y ?$

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