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Question Number 125411 Answers: 0 Comments: 0

Σ_(n=1) ^∞ ((√n)/(n^2 +1))

$$\underset{{n}=\mathrm{1}} {\overset{\infty} {\sum}}\frac{\sqrt{{n}}}{{n}^{\mathrm{2}} +\mathrm{1}} \\ $$

Question Number 125283 Answers: 0 Comments: 0

∫_0 ^1 ((x^2 sin^2 (log(x+1)))/((1+(√(1+x)))^2 ))dx

$$\int_{\mathrm{0}} ^{\mathrm{1}} \frac{{x}^{\mathrm{2}} {sin}^{\mathrm{2}} \left({log}\left({x}+\mathrm{1}\right)\right)}{\left(\mathrm{1}+\sqrt{\mathrm{1}+{x}}\right)^{\mathrm{2}} }{dx} \\ $$

Question Number 125167 Answers: 0 Comments: 1

f(x)=∫((cos(sinx)+cos^2 x)/(1+sinxsin(sinx)))dx Find f(1)

$${f}\left({x}\right)=\int\frac{{cos}\left({sinx}\right)+{cos}^{\mathrm{2}} {x}}{\mathrm{1}+{sinxsin}\left({sinx}\right)}{dx} \\ $$$${Find}\:{f}\left(\mathrm{1}\right) \\ $$

Question Number 125086 Answers: 0 Comments: 1

Question Number 125014 Answers: 0 Comments: 0

Question Number 124892 Answers: 0 Comments: 2

1−(1/(3.3!))+(1/(5.5!))−(1/(7.7!))+...

$$\mathrm{1}−\frac{\mathrm{1}}{\mathrm{3}.\mathrm{3}!}+\frac{\mathrm{1}}{\mathrm{5}.\mathrm{5}!}−\frac{\mathrm{1}}{\mathrm{7}.\mathrm{7}!}+... \\ $$

Question Number 124891 Answers: 0 Comments: 0

∫_0 ^(π/(24)) log(tanθ)dθ

$$\int_{\mathrm{0}} ^{\frac{\pi}{\mathrm{24}}} {log}\left({tan}\theta\right){d}\theta \\ $$

Question Number 124861 Answers: 0 Comments: 0

((((1/2))!)/(((3/2))!))−((((3/2))!1!)/(((5/2))!))+((((5/2))!2!)/(((7/2))!))−....

$$\frac{\left(\frac{\mathrm{1}}{\mathrm{2}}\right)!}{\left(\frac{\mathrm{3}}{\mathrm{2}}\right)!}−\frac{\left(\frac{\mathrm{3}}{\mathrm{2}}\right)!\mathrm{1}!}{\left(\frac{\mathrm{5}}{\mathrm{2}}\right)!}+\frac{\left(\frac{\mathrm{5}}{\mathrm{2}}\right)!\mathrm{2}!}{\left(\frac{\mathrm{7}}{\mathrm{2}}\right)!}−.... \\ $$

Question Number 124718 Answers: 0 Comments: 1

Σ_(n=1) ^n n^2 log(n+1) (In explicit form )

$$\underset{{n}=\mathrm{1}} {\overset{{n}} {\sum}}{n}^{\mathrm{2}} {log}\left({n}+\mathrm{1}\right)\:\:\:\:\left({In}\:{explicit}\:{form}\:\right) \\ $$

Question Number 124642 Answers: 0 Comments: 0

Evaluate : ∫ (4/( (√(2−((1/( ((x^2 + 1))^(1/3) )))^4 ))))dx

$$\: \\ $$$$\:\:\:{Evaluate}\::\: \\ $$$$\:\:\:\int\:\frac{\mathrm{4}}{\:\sqrt{\mathrm{2}−\left(\frac{\mathrm{1}}{\:\sqrt[{\mathrm{3}}]{{x}^{\mathrm{2}} \:+\:\mathrm{1}}}\right)^{\mathrm{4}} }}{dx} \\ $$

Question Number 124595 Answers: 4 Comments: 0

Given that ω = e^(iθ) , θ≠ nπ, n ∈ N show that (1) ((ω^2 −1)/ω) = 2i sin θ (2) (1 + ω)^n = 2^n cos^n ((1/2)θ)e^((1/2)(inθ))

$$\mathrm{Given}\:\mathrm{that}\:\:\omega\:=\:{e}^{{i}\theta} ,\:\theta\neq\:{n}\pi,\:{n}\:\in\:\mathbb{N} \\ $$$$\mathrm{show}\:\mathrm{that}\: \\ $$$$\:\left(\mathrm{1}\right)\:\frac{\omega^{\mathrm{2}} −\mathrm{1}}{\omega}\:=\:\mathrm{2}{i}\:\mathrm{sin}\:\theta \\ $$$$\:\left(\mathrm{2}\right)\:\left(\mathrm{1}\:+\:\omega\right)^{{n}} \:=\:\mathrm{2}^{{n}} \mathrm{cos}^{{n}} \left(\frac{\mathrm{1}}{\mathrm{2}}\theta\right){e}^{\frac{\mathrm{1}}{\mathrm{2}}\left({in}\theta\right)} \\ $$

Question Number 124528 Answers: 0 Comments: 0

Question Number 124487 Answers: 1 Comments: 1

Question Number 124474 Answers: 1 Comments: 1

((4/(−6+i(√5))))^4 =??? polar????

$$\left(\frac{\mathrm{4}}{−\mathrm{6}+{i}\sqrt{\mathrm{5}}}\right)^{\mathrm{4}} =??? \\ $$$$ \\ $$$${polar}???? \\ $$

Question Number 124461 Answers: 2 Comments: 2

∫_0 ^∞ e^(−x^7 ) sin(x^7 )dx

$$\int_{\mathrm{0}} ^{\infty} {e}^{−{x}^{\mathrm{7}} } {sin}\left({x}^{\mathrm{7}} \right){dx} \\ $$

Question Number 124459 Answers: 1 Comments: 1

1−(1/2)((1/2))+(1/4)((1/2).(3/4))−(1/8)(((1.3.5)/(2.4.6)))+...

$$\mathrm{1}−\frac{\mathrm{1}}{\mathrm{2}}\left(\frac{\mathrm{1}}{\mathrm{2}}\right)+\frac{\mathrm{1}}{\mathrm{4}}\left(\frac{\mathrm{1}}{\mathrm{2}}.\frac{\mathrm{3}}{\mathrm{4}}\right)−\frac{\mathrm{1}}{\mathrm{8}}\left(\frac{\mathrm{1}.\mathrm{3}.\mathrm{5}}{\mathrm{2}.\mathrm{4}.\mathrm{6}}\right)+... \\ $$

Question Number 124347 Answers: 1 Comments: 1

Question Number 124321 Answers: 2 Comments: 0

f(x,y,z)=z^2 yz^3 A=xzi−y^2 j+2x^2 yk div(fA)=? curl(fA)=?

$${f}\left({x},{y},{z}\right)={z}^{\mathrm{2}} {yz}^{\mathrm{3}} \\ $$$${A}={xzi}−{y}^{\mathrm{2}} {j}+\mathrm{2}{x}^{\mathrm{2}} {yk} \\ $$$${div}\left({fA}\right)=? \\ $$$${curl}\left({fA}\right)=? \\ $$

Question Number 124320 Answers: 2 Comments: 0

z+(1/z)=1 z^3 =??

$${z}+\frac{\mathrm{1}}{{z}}=\mathrm{1} \\ $$$${z}^{\mathrm{3}} =?? \\ $$

Question Number 124300 Answers: 0 Comments: 0

Question Number 124302 Answers: 1 Comments: 0

n=2^(n−1) sin((π/n))sin(((2π)/n))....sin(((n−1)/n)π) prove

$${n}=\mathrm{2}^{{n}−\mathrm{1}} {sin}\left(\frac{\pi}{{n}}\right){sin}\left(\frac{\mathrm{2}\pi}{{n}}\right)....{sin}\left(\frac{{n}−\mathrm{1}}{{n}}\pi\right)\:\:{prove}\: \\ $$$$ \\ $$

Question Number 124271 Answers: 0 Comments: 0

Question Number 124178 Answers: 1 Comments: 6

∫_0 ^(π/2) (1/( (√(cos^4 x+sin^4 x))))dx

$$\int_{\mathrm{0}} ^{\frac{\pi}{\mathrm{2}}} \frac{\mathrm{1}}{\:\sqrt{{cos}^{\mathrm{4}} {x}+{sin}^{\mathrm{4}} {x}}}{dx} \\ $$

Question Number 123947 Answers: 0 Comments: 0

((9^2 −1^2 )/(9^2 −2^2 )).((18^2 −1^2 )/(18^2 −0^2 )).((27^2 −1^2 )/(27^2 −2^2 )).((36^2 −1^2 )/(36^2 −0^2 )).....

$$\frac{\mathrm{9}^{\mathrm{2}} −\mathrm{1}^{\mathrm{2}} }{\mathrm{9}^{\mathrm{2}} −\mathrm{2}^{\mathrm{2}} }.\frac{\mathrm{18}^{\mathrm{2}} −\mathrm{1}^{\mathrm{2}} }{\mathrm{18}^{\mathrm{2}} −\mathrm{0}^{\mathrm{2}} }.\frac{\mathrm{27}^{\mathrm{2}} −\mathrm{1}^{\mathrm{2}} }{\mathrm{27}^{\mathrm{2}} −\mathrm{2}^{\mathrm{2}} }.\frac{\mathrm{36}^{\mathrm{2}} −\mathrm{1}^{\mathrm{2}} }{\mathrm{36}^{\mathrm{2}} −\mathrm{0}^{\mathrm{2}} }..... \\ $$

Question Number 123845 Answers: 1 Comments: 1

Question Number 123823 Answers: 1 Comments: 0

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