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Question Number 167773 Answers: 2 Comments: 0

Calculate ∫((xtan x)/(cos^4 x))dx

$${Calculate} \\ $$$$\int\frac{{x}\mathrm{tan}\:{x}}{\mathrm{cos}\:^{\mathrm{4}} {x}}{dx} \\ $$

Question Number 167757 Answers: 1 Comments: 1

Calculate ∫sec^2 xsec xdx

$${Calculate} \\ $$$$\int\mathrm{sec}\:^{\mathrm{2}} {x}\mathrm{sec}\:{xdx} \\ $$

Question Number 167746 Answers: 1 Comments: 1

log_((x^2 +2)) (x^2 +4x)=?

$${log}_{\left({x}^{\mathrm{2}} +\mathrm{2}\right)} \left({x}^{\mathrm{2}} +\mathrm{4}{x}\right)=? \\ $$

Question Number 167740 Answers: 0 Comments: 0

I_n =∫_0 ^(π/4) (1/(cos^(2n+1) x))dx Prove by parts that: 2nI_n =(2n−1)I_(n−1) +(2^n /( (√2)))

$${I}_{{n}} =\int_{\mathrm{0}} ^{\frac{\pi}{\mathrm{4}}} \frac{\mathrm{1}}{\mathrm{cos}\:^{\mathrm{2}{n}+\mathrm{1}} {x}}{dx} \\ $$$${Prove}\:{by}\:{parts}\:{that}: \\ $$$$\mathrm{2}{nI}_{{n}} =\left(\mathrm{2}{n}−\mathrm{1}\right){I}_{{n}−\mathrm{1}} +\frac{\mathrm{2}^{{n}} }{\:\sqrt{\mathrm{2}}} \\ $$

Question Number 167739 Answers: 4 Comments: 2

Question Number 167738 Answers: 2 Comments: 0

72 → 49 42 → 16 21 → 2 16 → ?

$$\mathrm{72}\:\:\:\rightarrow\:\:\:\mathrm{49} \\ $$$$\mathrm{42}\:\:\:\rightarrow\:\:\:\mathrm{16} \\ $$$$\mathrm{21}\:\:\:\rightarrow\:\:\:\mathrm{2} \\ $$$$\mathrm{16}\:\:\:\rightarrow\:\:\:? \\ $$

Question Number 167737 Answers: 1 Comments: 0

3 □ 4 → 27 4 □ 2 → 36 2 □ 7 → 18 1 □ 9 → ?

$$\mathrm{3}\:\:\:\Box\:\:\:\mathrm{4}\:\:\:\rightarrow\:\:\:\mathrm{27} \\ $$$$\mathrm{4}\:\:\:\Box\:\:\:\mathrm{2}\:\:\:\rightarrow\:\:\:\mathrm{36} \\ $$$$\mathrm{2}\:\:\:\Box\:\:\:\mathrm{7}\:\:\:\rightarrow\:\:\:\mathrm{18} \\ $$$$\mathrm{1}\:\:\:\Box\:\:\:\mathrm{9}\:\:\:\rightarrow\:\:\:? \\ $$

Question Number 167730 Answers: 1 Comments: 2

Question Number 167772 Answers: 1 Comments: 2

x+(√x)=5 x+(5/( (√x)))=?

$${x}+\sqrt{{x}}=\mathrm{5} \\ $$$${x}+\frac{\mathrm{5}}{\:\sqrt{{x}}}=? \\ $$

Question Number 167750 Answers: 1 Comments: 0

Question Number 167725 Answers: 1 Comments: 4

Q#167612 reposted. Determine all the possible triples (a,b,c) of positive integers for which ab−c,bc−a and ca−b are powers of 2.

$${Q}#\mathrm{167612}\:{reposted}. \\ $$$$\mathcal{D}{etermine}\:{all}\:{the}\:{possible}\:{triples} \\ $$$$\left({a},{b},{c}\right)\:{of}\:{positive}\:{integers}\:{for}\:{which} \\ $$$${ab}−{c},{bc}−{a}\:{and}\:{ca}−{b}\:{are}\:{powers}\:{of} \\ $$$$\mathrm{2}. \\ $$

Question Number 167722 Answers: 1 Comments: 1

(2/Z) = (1/a)+(1/b) Z = ??? help

$$\frac{\mathrm{2}}{\boldsymbol{\mathrm{Z}}}\:=\:\frac{\mathrm{1}}{\boldsymbol{\mathrm{a}}}+\frac{\mathrm{1}}{\boldsymbol{\mathrm{b}}} \\ $$$$\boldsymbol{\mathrm{Z}}\:=\:???\:{help} \\ $$

Question Number 167718 Answers: 0 Comments: 2

(x−3)^2 +(y−5)^2 +(z−4)^2 =0 (x^2 /9)+(y^2 /(25))+(z^2 /(16))=? help me

$$\left({x}−\mathrm{3}\right)^{\mathrm{2}} +\left({y}−\mathrm{5}\right)^{\mathrm{2}} +\left({z}−\mathrm{4}\right)^{\mathrm{2}} =\mathrm{0} \\ $$$$\frac{{x}^{\mathrm{2}} }{\mathrm{9}}+\frac{{y}^{\mathrm{2}} }{\mathrm{25}}+\frac{{z}^{\mathrm{2}} }{\mathrm{16}}=? \\ $$$${help}\:{me} \\ $$

Question Number 167716 Answers: 1 Comments: 0

Question Number 167713 Answers: 1 Comments: 0

Question Number 167709 Answers: 0 Comments: 0

Question Number 167700 Answers: 1 Comments: 0

Evalvate the following integrals: 1. ∫(√(x^3 + 6x^2 + 9x dx)) 2. ∫ (((x - 6) dx)/(x^4 - 24x + 3))

$$\mathrm{Evalvate}\:\mathrm{the}\:\mathrm{following}\:\mathrm{integrals}: \\ $$$$\mathrm{1}.\:\int\sqrt{\mathrm{x}^{\mathrm{3}} \:+\:\mathrm{6x}^{\mathrm{2}} \:+\:\mathrm{9x}\:\mathrm{dx}} \\ $$$$\mathrm{2}.\:\int\:\frac{\left(\mathrm{x}\:-\:\mathrm{6}\right)\:\mathrm{dx}}{\mathrm{x}^{\mathrm{4}} \:-\:\mathrm{24x}\:+\:\mathrm{3}} \\ $$

Question Number 167699 Answers: 4 Comments: 0

Question Number 167696 Answers: 1 Comments: 0

solv: e^x +x+1=0

$${solv}:\:\: \\ $$$${e}^{{x}} +{x}+\mathrm{1}=\mathrm{0} \\ $$

Question Number 167690 Answers: 1 Comments: 0

Question Number 167682 Answers: 1 Comments: 1

solve: 2^x +3^x =5^x

$${solve}:\:\mathrm{2}^{{x}} +\mathrm{3}^{{x}} =\mathrm{5}^{{x}} \\ $$

Question Number 167662 Answers: 1 Comments: 0

lim_(x→3) [((log((2log(√(x^3 +2))))^(1/3) ))^(1/4) ]=?

$$\underset{{x}\rightarrow\mathrm{3}} {\mathrm{lim}}\left[\sqrt[{\mathrm{4}}]{{log}\sqrt[{\mathrm{3}}]{\mathrm{2}{log}\sqrt{{x}^{\mathrm{3}} +\mathrm{2}}}}\right]=? \\ $$

Question Number 167666 Answers: 1 Comments: 1

I_n =∫(dx/(cos^n x)) Prove that I_n =((n−2)/(n−1))I_(n−2) +((sin x)/((n−1)cos^(n−1) x))

$${I}_{{n}} =\int\frac{{dx}}{\mathrm{cos}\:^{{n}} {x}} \\ $$$${Prove}\:{that} \\ $$$${I}_{{n}} =\frac{{n}−\mathrm{2}}{{n}−\mathrm{1}}{I}_{{n}−\mathrm{2}} +\frac{\mathrm{sin}\:{x}}{\left({n}−\mathrm{1}\right)\mathrm{cos}\:^{{n}−\mathrm{1}} {x}} \\ $$

Question Number 167664 Answers: 0 Comments: 0

a=3k,b=4k,c=5k 3k+4k+5k=1000⇒k=500/6 a=1500/6,b=200/6,c=2500/6

$${a}=\mathrm{3}{k},{b}=\mathrm{4}{k},{c}=\mathrm{5}{k} \\ $$$$\mathrm{3}{k}+\mathrm{4}{k}+\mathrm{5}{k}=\mathrm{1000}\Rightarrow{k}=\mathrm{500}/\mathrm{6} \\ $$$${a}=\mathrm{1500}/\mathrm{6},{b}=\mathrm{200}/\mathrm{6},{c}=\mathrm{2500}/\mathrm{6} \\ $$

Question Number 167663 Answers: 1 Comments: 2

lim_(x→2) [log((1/x)+(1/(2x))+(1/(4x)).......)]=?

$$\underset{{x}\rightarrow\mathrm{2}} {\mathrm{lim}}\left[{log}\left(\frac{\mathrm{1}}{{x}}+\frac{\mathrm{1}}{\mathrm{2}{x}}+\frac{\mathrm{1}}{\mathrm{4}{x}}.......\right)\right]=? \\ $$

Question Number 167650 Answers: 1 Comments: 4

{: (( a^2 +b^2 =c^2 )),((a+b+c=1000)) }; a^(?) , b^(?) , c^(?) ∈Z Q#167533 reposted

$$\left.\begin{matrix}{\:\:\:\:\:\:\:\:\:{a}^{\mathrm{2}} +{b}^{\mathrm{2}} ={c}^{\mathrm{2}} }\\{{a}+{b}+{c}=\mathrm{1000}}\end{matrix}\right\};\:\overset{?} {{a}},\:\:\overset{?} {{b}},\:\:\overset{?} {{c}}\in\mathbb{Z} \\ $$$${Q}#\mathrm{167533}\:\mathrm{reposted} \\ $$

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