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AllQuestion and Answers: Page 1149

Question Number 101633 Answers: 1 Comments: 2

∫x^x^x ∙x^x ∙x dx=?

$$\int\mathrm{x}^{\mathrm{x}^{\mathrm{x}} } \centerdot\mathrm{x}^{\mathrm{x}} \centerdot\mathrm{x}\:\mathrm{dx}=? \\ $$

Question Number 101625 Answers: 0 Comments: 1

Question Number 101615 Answers: 3 Comments: 4

Question Number 101616 Answers: 2 Comments: 1

Question Number 101610 Answers: 2 Comments: 0

Question Number 101608 Answers: 0 Comments: 0

∫_(0 ) ^(π/2) ln(((ln^2 (sin(θ)))/(π^2 +ln^2 (sin(θ)))))((ln(cos(θ)))/(tan(θ)))dθ

$$\int_{\mathrm{0}\:} ^{\frac{\pi}{\mathrm{2}}} {ln}\left(\frac{{ln}^{\mathrm{2}} \left({sin}\left(\theta\right)\right)}{\pi^{\mathrm{2}} +{ln}^{\mathrm{2}} \left({sin}\left(\theta\right)\right)}\right)\frac{{ln}\left({cos}\left(\theta\right)\right)}{{tan}\left(\theta\right)}{d}\theta \\ $$

Question Number 101607 Answers: 0 Comments: 0

f(x)=(√(2x+7))+log_3 x f^(−1) (x)=?

$$\mathrm{f}\left(\mathrm{x}\right)=\sqrt{\mathrm{2x}+\mathrm{7}}+\mathrm{log}_{\mathrm{3}} \mathrm{x} \\ $$$$\mathrm{f}^{−\mathrm{1}} \left(\mathrm{x}\right)=?\:\:\:\:\:\: \\ $$

Question Number 101601 Answers: 1 Comments: 0

∫_((√2)−1) ^((√2)+1) ((x^4 +x^2 +1)/((x^2 +1)^2 ))dx

$$\int_{\sqrt{\mathrm{2}}−\mathrm{1}} ^{\sqrt{\mathrm{2}}+\mathrm{1}} \frac{{x}^{\mathrm{4}} +{x}^{\mathrm{2}} +\mathrm{1}}{\left({x}^{\mathrm{2}} +\mathrm{1}\right)^{\mathrm{2}} }{dx} \\ $$

Question Number 101597 Answers: 0 Comments: 3

∫ ln (1+ e^x ) dx = ..

$$\:\int\:\mathrm{ln}\:\left(\mathrm{1}+\:{e}^{{x}} \right)\:{dx}\:=\:.. \\ $$

Question Number 101595 Answers: 2 Comments: 0

let f(x) =cos^n x 1) find f^((n)) (x) and f^((n)) (0) 2) developp f at integr serie 3) detemine ∫ f(x)dx

$$\mathrm{let}\:\mathrm{f}\left(\mathrm{x}\right)\:=\mathrm{cos}^{\mathrm{n}} \mathrm{x} \\ $$$$\left.\mathrm{1}\right)\:\mathrm{find}\:\mathrm{f}^{\left(\mathrm{n}\right)} \left(\mathrm{x}\right)\:\mathrm{and}\:\mathrm{f}^{\left(\mathrm{n}\right)} \left(\mathrm{0}\right) \\ $$$$\left.\mathrm{2}\right)\:\mathrm{developp}\:\mathrm{f}\:\mathrm{at}\:\mathrm{integr}\:\mathrm{serie} \\ $$$$\left.\mathrm{3}\right)\:\mathrm{detemine}\:\:\int\:\mathrm{f}\left(\mathrm{x}\right)\mathrm{dx} \\ $$

Question Number 101585 Answers: 1 Comments: 0

∫_0 ^π (1/(a^2 −2a cosx + 1))dx (a<1) is

$$\int_{\mathrm{0}} ^{\pi} \frac{\mathrm{1}}{{a}^{\mathrm{2}} −\mathrm{2}{a}\:{cosx}\:+\:\mathrm{1}}{dx}\:\left({a}<\mathrm{1}\right)\:{is} \\ $$$$ \\ $$

Question Number 101582 Answers: 2 Comments: 0

lim_(n→∞) (1/n^2 ) Σ_(r=1) ^n r e^(r/n) =

$$\underset{{n}\rightarrow\infty} {\mathrm{lim}}\:\:\frac{\mathrm{1}}{{n}^{\mathrm{2}} }\:\underset{{r}=\mathrm{1}} {\overset{{n}} {\sum}}\:{r}\:{e}^{{r}/{n}} \:= \\ $$

Question Number 101590 Answers: 2 Comments: 1

p(2x+5)=(2x^2 +3x−1)Q(x+1) if Q(−1)=3 then p(1)=?

$$\mathrm{p}\left(\mathrm{2x}+\mathrm{5}\right)=\left(\mathrm{2x}^{\mathrm{2}} +\mathrm{3x}−\mathrm{1}\right)\mathrm{Q}\left(\mathrm{x}+\mathrm{1}\right) \\ $$$$\mathrm{if}\:\mathrm{Q}\left(−\mathrm{1}\right)=\mathrm{3}\:\:\:\:\:\mathrm{then}\:\mathrm{p}\left(\mathrm{1}\right)=? \\ $$

Question Number 101589 Answers: 1 Comments: 0

if sin10^0 =x then sin70^0 =?

$$\mathrm{if}\:\mathrm{sin10}^{\mathrm{0}} =\mathrm{x}\:\:\:\:\:\:\:\:\:\:\mathrm{then}\:\:\:\mathrm{sin70}^{\mathrm{0}} =? \\ $$

Question Number 101871 Answers: 1 Comments: 0

if a_1 = −4 , a_2 =−1 and a_n = a_(n+1) +a_(n+3 ) . find a_4 −a_1 ?

$${if}\:{a}_{\mathrm{1}} =\:−\mathrm{4}\:,\:{a}_{\mathrm{2}} =−\mathrm{1}\:{and}\: \\ $$$${a}_{{n}} \:=\:{a}_{{n}+\mathrm{1}} +{a}_{{n}+\mathrm{3}\:} .\:{find}\: \\ $$$${a}_{\mathrm{4}} −{a}_{\mathrm{1}} ? \\ $$

Question Number 101860 Answers: 1 Comments: 1

Question Number 101851 Answers: 1 Comments: 0

Question Number 101568 Answers: 1 Comments: 0

Question Number 101563 Answers: 2 Comments: 0

Question Number 101558 Answers: 1 Comments: 0

if y=sin2x is the solution of differintial equation (d^2 y/dx^2 ) +4y=k then the k is .......

$${if}\:{y}={sin}\mathrm{2}{x}\:{is}\:{the}\:{solution}\:{of}\:{differintial}\:{equation}\: \\ $$$$\frac{{d}^{\mathrm{2}} {y}}{{dx}^{\mathrm{2}} }\:+\mathrm{4}{y}={k}\:{then}\:{the}\:{k}\:{is}\:....... \\ $$

Question Number 101555 Answers: 1 Comments: 0

Question Number 101554 Answers: 3 Comments: 0

(1/(cos80))−((√3)/(sin80))=?

$$\frac{\mathrm{1}}{\mathrm{cos80}}−\frac{\sqrt{\mathrm{3}}}{\mathrm{sin80}}=? \\ $$

Question Number 101553 Answers: 1 Comments: 0

solve the inequality (^3 log x+2)^(5x+1) ≥ (^3 log x +2)^(3−3x)

$$\mathrm{solve}\:\mathrm{the}\:\mathrm{inequality} \\ $$$$\left(\:^{\mathrm{3}} \mathrm{log}\:{x}+\mathrm{2}\right)^{\mathrm{5}{x}+\mathrm{1}} \:\geqslant\:\left(\:^{\mathrm{3}} \mathrm{log}\:{x}\:+\mathrm{2}\right)^{\mathrm{3}−\mathrm{3}{x}} \\ $$

Question Number 101551 Answers: 2 Comments: 0

Question Number 101546 Answers: 4 Comments: 1

Question Number 101531 Answers: 1 Comments: 0

find ∫(√(ax−x^2 ))dx

$${find}\:\int\sqrt{{ax}−{x}^{\mathrm{2}} }{dx} \\ $$

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