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IntegrationQuestion and Answers: Page 199

Question Number 83440 Answers: 0 Comments: 0

find ∫_0 ^(π/2) (dx/(sinx^(cosx) +cosx^(sinx) ))

$${find}\:\int_{\mathrm{0}} ^{\frac{\pi}{\mathrm{2}}} \:\frac{{dx}}{{sinx}^{{cosx}} +{cosx}^{{sinx}} } \\ $$

Question Number 83405 Answers: 0 Comments: 2

lim_(b→1^− ) ∫_0 ^b ((sin (x))/(√(1−x^2 ))) dx ?

$$\underset{\mathrm{b}\rightarrow\mathrm{1}^{−} } {\mathrm{lim}}\:\int_{\mathrm{0}} ^{\mathrm{b}} \:\frac{\mathrm{sin}\:\left(\mathrm{x}\right)}{\sqrt{\mathrm{1}−\mathrm{x}^{\mathrm{2}} }}\:\mathrm{dx}\:?\: \\ $$

Question Number 83385 Answers: 2 Comments: 1

∫((1+ae^(−(a+1)x) +(a+1)e^(−ax) )/x^2 ) dx, a∈z^+

$$\int\frac{\mathrm{1}+{ae}^{−\left({a}+\mathrm{1}\right){x}} +\left({a}+\mathrm{1}\right){e}^{−{ax}} }{{x}^{\mathrm{2}} }\:{dx},\:\:{a}\in{z}^{+} \\ $$

Question Number 83383 Answers: 1 Comments: 0

find ∫_0 ^2 ∫_0 ^(√(4−x^2 )) ∫_0 ^(2−z) zdxdydz pleas help me sir

$${find}\:\int_{\mathrm{0}} ^{\mathrm{2}} \int_{\mathrm{0}} ^{\sqrt{\mathrm{4}−{x}^{\mathrm{2}} }} \int_{\mathrm{0}} ^{\mathrm{2}−{z}} {zdxdydz} \\ $$$${pleas}\:{help}\:{me}\:{sir} \\ $$

Question Number 83367 Answers: 0 Comments: 1

∫_(−∞) ^∞ ((sin^7 (x))/x^7 )dx

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

Question Number 83342 Answers: 1 Comments: 0

∫_0 ^1 ∫_0 ^( z) ∫_y ^1 ((z^(n+1) Li_1 (y))/((zx)^2 ))dx dy dz , ∀ n∈z

$$\int_{\mathrm{0}} ^{\mathrm{1}} \int_{\mathrm{0}} ^{\:{z}} \int_{{y}} ^{\mathrm{1}} \frac{{z}^{{n}+\mathrm{1}} {Li}_{\mathrm{1}} \left({y}\right)}{\left({zx}\right)^{\mathrm{2}} }{dx}\:{dy}\:{dz}\:,\:\forall\:{n}\in{z} \\ $$

Question Number 83338 Answers: 1 Comments: 0

∫ sin (3x) tan (2x) dx ?

$$\int\:\mathrm{sin}\:\left(\mathrm{3x}\right)\:\mathrm{tan}\:\left(\mathrm{2x}\right)\:\mathrm{dx}\:? \\ $$

Question Number 83331 Answers: 1 Comments: 7

Question Number 83318 Answers: 0 Comments: 0

Evaluate ∫x^(1/x^n ) dx ,n>0

$${Evaluate} \\ $$$$\int{x}^{\frac{\mathrm{1}}{{x}^{{n}} }} \:{dx}\:,{n}>\mathrm{0} \\ $$

Question Number 83276 Answers: 1 Comments: 0

∫sec^5 3x•sec3xtan 3xdx

$$\int\mathrm{s}{ec}^{\mathrm{5}} \mathrm{3}{x}\bullet\mathrm{s}{ec}\mathrm{3}{x}\mathrm{tan}\:\mathrm{3}{xdx} \\ $$

Question Number 83259 Answers: 1 Comments: 0

∫x^9 sin x^(10) dx

$$\int{x}^{\mathrm{9}} \mathrm{sin}\:{x}^{\mathrm{10}} {dx} \\ $$

Question Number 83253 Answers: 0 Comments: 3

calculate ∫_0 ^∞ (dx/((x^4 −x^2 +1)^2 ))

$${calculate}\:\int_{\mathrm{0}} ^{\infty} \:\frac{{dx}}{\left({x}^{\mathrm{4}} −{x}^{\mathrm{2}} \:+\mathrm{1}\right)^{\mathrm{2}} } \\ $$

Question Number 83252 Answers: 1 Comments: 1

calculate ∫_0 ^(π/2) (dx/(cos^2 x +(√3)sin^2 x))

$${calculate}\:\int_{\mathrm{0}} ^{\frac{\pi}{\mathrm{2}}} \:\frac{{dx}}{{cos}^{\mathrm{2}} {x}\:+\sqrt{\mathrm{3}}{sin}^{\mathrm{2}} {x}} \\ $$

Question Number 83251 Answers: 0 Comments: 1

calculate ∫ ch^2 (x)sin^3 xdx

$${calculate}\:\:\int\:\:{ch}^{\mathrm{2}} \left({x}\right){sin}^{\mathrm{3}} \:{xdx} \\ $$

Question Number 83250 Answers: 1 Comments: 0

1)decompose F(x)=((x^2 −3)/(2x^3 +5x+7)) 2)determine ∫ F(x)dx

$$\left.\mathrm{1}\right){decompose}\:{F}\left({x}\right)=\frac{{x}^{\mathrm{2}} −\mathrm{3}}{\mathrm{2}{x}^{\mathrm{3}} \:+\mathrm{5}{x}+\mathrm{7}} \\ $$$$\left.\mathrm{2}\right){determine}\:\int\:{F}\left({x}\right){dx} \\ $$

Question Number 83246 Answers: 0 Comments: 0

fnd ∫ xe^(−x^2 ) arctan(1−(1/x))dx

$${fnd}\:\int\:{xe}^{−{x}^{\mathrm{2}} } {arctan}\left(\mathrm{1}−\frac{\mathrm{1}}{{x}}\right){dx} \\ $$

Question Number 83206 Answers: 0 Comments: 2

1) find ∫_0 ^(π/4) (dx/(2+a sinx)) (areal) 2) c explicite ∫_0 ^(π/4) ((sinx)/((2+asinx)^2 ))dx

$$\left.\mathrm{1}\right)\:{find}\:\int_{\mathrm{0}} ^{\frac{\pi}{\mathrm{4}}} \:\frac{{dx}}{\mathrm{2}+{a}\:{sinx}}\:\:\:\:\left({areal}\right) \\ $$$$\left.\mathrm{2}\right)\:{c}\:{explicite}\:\int_{\mathrm{0}} ^{\frac{\pi}{\mathrm{4}}} \:\frac{{sinx}}{\left(\mathrm{2}+{asinx}\right)^{\mathrm{2}} }{dx} \\ $$

Question Number 83204 Answers: 0 Comments: 1

∫_(t−1) ^t ln(x!)dx=?

$$\int_{{t}−\mathrm{1}} ^{{t}} {ln}\left({x}!\right){dx}=? \\ $$

Question Number 83164 Answers: 2 Comments: 2

Evaluate: ∫_0 ^( (π/2)) (( 1)/(1+cos 𝛂 cos x))dx

$$ \\ $$$$ \\ $$$$\:\mathrm{Evaluate}: \\ $$$$\:\:\int_{\mathrm{0}} ^{\:\frac{\pi}{\mathrm{2}}} \:\frac{\:\:\mathrm{1}}{\mathrm{1}+\boldsymbol{\mathrm{cos}}\:\boldsymbol{\alpha}\:\boldsymbol{\mathrm{cos}}\:\boldsymbol{\mathrm{x}}}\boldsymbol{\mathrm{dx}} \\ $$

Question Number 83123 Answers: 0 Comments: 6

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

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

Question Number 83115 Answers: 1 Comments: 1

∫cos xe^(sin x) dx

$$\int\mathrm{cos}\:{xe}^{\mathrm{sin}\:{x}} {dx} \\ $$

Question Number 83110 Answers: 0 Comments: 10

bounded by the curve y=(√(4-x)) y=0 y=1

$${bounded}\:{by}\:{the}\:{curve}\:{y}=\sqrt{\mathrm{4}-{x}}\:{y}=\mathrm{0}\:{y}=\mathrm{1} \\ $$

Question Number 83109 Answers: 0 Comments: 1

∫_(1/e) ^e (dt/t)

$$\int_{\mathrm{1}/\boldsymbol{{e}}} ^{{e}} \frac{\boldsymbol{{dt}}}{\boldsymbol{{t}}} \\ $$

Question Number 83108 Answers: 1 Comments: 0

prove that ∫_0 ^(π/4) ((cos(nx))/(cos^n (x))) dx =2^n [(π/8)−Σ_(k=1) ^(n−1) ((sin(((kπ)/4)))/(2k((√2))^k ))] n∈N^∗

$${prove}\:{that} \\ $$$$\int_{\mathrm{0}} ^{\frac{\pi}{\mathrm{4}}} \frac{{cos}\left({nx}\right)}{{cos}^{{n}} \left({x}\right)}\:{dx}\:=\mathrm{2}^{{n}} \left[\frac{\pi}{\mathrm{8}}−\underset{{k}=\mathrm{1}} {\overset{{n}−\mathrm{1}} {\sum}}\frac{{sin}\left(\frac{{k}\pi}{\mathrm{4}}\right)}{\mathrm{2}{k}\left(\sqrt{\mathrm{2}}\right)^{{k}} }\right]\:{n}\in{N}^{\ast} \\ $$

Question Number 83104 Answers: 1 Comments: 0

∫((e^x dx)/(3+e^x ))

$$\int\frac{{e}^{{x}} {dx}}{\mathrm{3}+{e}^{{x}} } \\ $$

Question Number 83096 Answers: 0 Comments: 1

∫tan x^4 dx

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

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