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IntegrationQuestion and Answers: Page 213

Question Number 74492 Answers: 0 Comments: 0

calculate ∫_0 ^∞ ((arctan(x^2 ))/(x^2 +9))dx

$${calculate}\:\int_{\mathrm{0}} ^{\infty} \:\:\frac{{arctan}\left({x}^{\mathrm{2}} \right)}{{x}^{\mathrm{2}} \:+\mathrm{9}}{dx} \\ $$

Question Number 74484 Answers: 0 Comments: 1

calculate ∫_0 ^∞ ((arctan(2x))/(x^2 +3))dx

$${calculate}\:\int_{\mathrm{0}} ^{\infty} \:\:\frac{{arctan}\left(\mathrm{2}{x}\right)}{{x}^{\mathrm{2}} +\mathrm{3}}{dx} \\ $$

Question Number 74446 Answers: 1 Comments: 0

Question Number 75089 Answers: 0 Comments: 4

∫sin (x^3 +c) dx=? ∫sinh (x^3 +c) dx=?

$$\int\mathrm{sin}\:\left({x}^{\mathrm{3}} +{c}\right)\:{dx}=? \\ $$$$\int\mathrm{sinh}\:\left({x}^{\mathrm{3}} +{c}\right)\:{dx}=? \\ $$

Question Number 74394 Answers: 1 Comments: 4

Question Number 74367 Answers: 0 Comments: 2

Solve : (D^4 +4)y=0 given: y(0)=0 , y′(0)=2 , y′′(0)=0 and y′′′(0)=4.

$${Solve}\:: \\ $$$$\left({D}^{\mathrm{4}} +\mathrm{4}\right){y}=\mathrm{0}\: \\ $$$${given}:\:{y}\left(\mathrm{0}\right)=\mathrm{0}\:,\:{y}'\left(\mathrm{0}\right)=\mathrm{2}\:,\:{y}''\left(\mathrm{0}\right)=\mathrm{0}\:{and} \\ $$$${y}'''\left(\mathrm{0}\right)=\mathrm{4}. \\ $$

Question Number 74395 Answers: 0 Comments: 2

calculate ∫_0 ^∞ e^(−2x) [e^x ]dx

$${calculate}\:\int_{\mathrm{0}} ^{\infty} \:\:\:{e}^{−\mathrm{2}{x}} \left[{e}^{{x}} \right]{dx} \\ $$

Question Number 74349 Answers: 0 Comments: 2

calculate ∫_0 ^∞ ((cos(2πx))/((x^2 +3)^2 ))dx

$${calculate}\:\int_{\mathrm{0}} ^{\infty} \:\frac{{cos}\left(\mathrm{2}\pi{x}\right)}{\left({x}^{\mathrm{2}} +\mathrm{3}\right)^{\mathrm{2}} }{dx} \\ $$

Question Number 74348 Answers: 0 Comments: 1

calculate ∫_0 ^∞ ((arctan(sin(x^2 )))/(x^2 +1))dx

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

Question Number 74347 Answers: 0 Comments: 0

calculate ∫_0 ^∞ ((arctan(cos(πx^2 )))/(x^2 +1))dx

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

Question Number 74346 Answers: 1 Comments: 0

find ∫ ((x+(√(x+1)))/(2(√(x−1))+3))dx

$${find}\:\int\:\:\frac{{x}+\sqrt{{x}+\mathrm{1}}}{\mathrm{2}\sqrt{{x}−\mathrm{1}}+\mathrm{3}}{dx} \\ $$

Question Number 74344 Answers: 1 Comments: 1

calculate ∫ ((x^2 −x+3)/(x^3 (x+2)^2 ))dx

$${calculate}\:\int\:\:\:\:\:\frac{{x}^{\mathrm{2}} −{x}+\mathrm{3}}{{x}^{\mathrm{3}} \left({x}+\mathrm{2}\right)^{\mathrm{2}} }{dx} \\ $$

Question Number 74343 Answers: 0 Comments: 1

calculatef(α)= ∫_0 ^∞ ((arctan(αx^2 ))/(x^2 +9))dx with α real.

$${calculatef}\left(\alpha\right)=\:\:\int_{\mathrm{0}} ^{\infty} \:\:\:\frac{{arctan}\left(\alpha{x}^{\mathrm{2}} \right)}{{x}^{\mathrm{2}} \:+\mathrm{9}}{dx}\:\:\:{with}\:\alpha\:{real}. \\ $$

Question Number 74334 Answers: 0 Comments: 1

∫te^t cos e^t .e^t dt

$$\int{te}^{{t}} \mathrm{cos}\:{e}^{{t}} .{e}^{{t}} {dt} \\ $$

Question Number 74320 Answers: 0 Comments: 0

∫_0 ^x x e^x (cos e^x )e^x dx

$$\int_{\mathrm{0}} ^{{x}} {x}\:{e}^{{x}} \left(\mathrm{cos}\:\:{e}^{{x}} \right){e}^{{x}} {dx} \\ $$

Question Number 74264 Answers: 0 Comments: 1

∫_0 ^x xe^x sin e^x e^x dx

$$\int_{\mathrm{0}} ^{{x}} {xe}^{{x}} \mathrm{sin}\:{e}^{{x}} {e}^{{x}} {dx} \\ $$

Question Number 74263 Answers: 0 Comments: 1

∫_0 ^x e^x cos e^x e^x dx

$$\int_{\mathrm{0}} ^{{x}} {e}^{{x}} \mathrm{cos}\:{e}^{{x}} {e}^{{x}} {dx} \\ $$

Question Number 74231 Answers: 1 Comments: 2

Question Number 74224 Answers: 1 Comments: 2

find ∫ (x^2 +1)^(1/4) cos((1/2)arctan((1/x)))dx and ∫ (x^2 +1)^(1/4) sin((1/2)arctan((1/x)))dx

$${find}\:\int\:\:\:\left({x}^{\mathrm{2}} +\mathrm{1}\right)^{\frac{\mathrm{1}}{\mathrm{4}}} \:{cos}\left(\frac{\mathrm{1}}{\mathrm{2}}{arctan}\left(\frac{\mathrm{1}}{{x}}\right)\right){dx}\:\:{and} \\ $$$$\int\:\:\left({x}^{\mathrm{2}} +\mathrm{1}\right)^{\frac{\mathrm{1}}{\mathrm{4}}} {sin}\left(\frac{\mathrm{1}}{\mathrm{2}}{arctan}\left(\frac{\mathrm{1}}{{x}}\right)\right){dx} \\ $$

Question Number 74223 Answers: 1 Comments: 0

calculate f(a)=∫_0 ^1 (√(x^2 +ax+1))dx and g(a)=∫_0 ^1 ((xdx)/(√(x^2 +ax+1))) with ∣a∣<2 2)find the value of ∫_0 ^1 (√(x^2 +(√2)x+1))dx and ∫_0 ^1 ((xdx)/(√(x^2 +(√2)x+1)))

$${calculate}\:\:{f}\left({a}\right)=\int_{\mathrm{0}} ^{\mathrm{1}} \sqrt{{x}^{\mathrm{2}} +{ax}+\mathrm{1}}{dx}\:\:\:{and}\:{g}\left({a}\right)=\int_{\mathrm{0}} ^{\mathrm{1}} \:\:\frac{{xdx}}{\sqrt{{x}^{\mathrm{2}} +{ax}+\mathrm{1}}} \\ $$$${with}\:\:\mid{a}\mid<\mathrm{2} \\ $$$$\left.\mathrm{2}\right){find}\:{the}\:{value}\:{of}\:\:\int_{\mathrm{0}} ^{\mathrm{1}} \sqrt{{x}^{\mathrm{2}} +\sqrt{\mathrm{2}}{x}+\mathrm{1}}{dx}\:{and}\:\int_{\mathrm{0}} ^{\mathrm{1}} \:\:\frac{{xdx}}{\sqrt{{x}^{\mathrm{2}} +\sqrt{\mathrm{2}}{x}+\mathrm{1}}} \\ $$

Question Number 74218 Answers: 1 Comments: 0

verify that y(x)=e^x (cos e^x −e^x sin e^x ) is the solution of integral equation y(x)=(1−xe^(2x) )cos 1−e^(2x) sin 1+∫_0 ^x {1−(x−t)e^(2x) }y(t)dt

$${verify}\:{that}\:{y}\left({x}\right)={e}^{{x}} \left(\mathrm{cos}\:{e}^{{x}} −{e}^{{x}} \mathrm{sin}\:{e}^{{x}} \right)\:{is}\:{the}\:{solution}\:{of}\:{integral}\:{equation}\:{y}\left({x}\right)=\left(\mathrm{1}−{xe}^{\mathrm{2}{x}} \right)\mathrm{cos}\:\mathrm{1}−{e}^{\mathrm{2}{x}} \mathrm{sin}\:\mathrm{1}+\underset{\mathrm{0}} {\overset{{x}} {\int}}\left\{\mathrm{1}−\left({x}−{t}\right){e}^{\mathrm{2}{x}} \right\}{y}\left({t}\right){dt} \\ $$

Question Number 74210 Answers: 1 Comments: 0

∫e^t cos e^t dt

$$\int{e}^{{t}} \mathrm{cos}\:{e}^{{t}} {dt} \\ $$

Question Number 74131 Answers: 0 Comments: 2

Can anyone share the solutions (pdf) of the book Advanced engineering Mathematics by Erwin kreyzig 8th edition ?

$${Can}\:{anyone}\:{share}\:{the}\:{solutions}\:\left({pdf}\right) \\ $$$${of}\:{the}\:{book}\:{Advanced}\:{engineering} \\ $$$${Mathematics}\:{by}\:{Erwin}\:{kreyzig}\:\mathrm{8}{th} \\ $$$${edition}\:? \\ $$$$ \\ $$

Question Number 74117 Answers: 0 Comments: 1

Find the volume of the solid that lies within the sphere x^2 +y^2 +z^2 =16, above the x-y plane and below the cone z=(√(x^2 +y^2 ))

$${Find}\:{the}\:{volume}\:{of}\:{the}\:{solid}\:{that}\:{lies} \\ $$$${within}\:{the}\:{sphere}\:{x}^{\mathrm{2}} +{y}^{\mathrm{2}} +{z}^{\mathrm{2}} =\mathrm{16},\:{above} \\ $$$${the}\:{x}-{y}\:{plane}\:{and}\:{below}\:{the}\:{cone} \\ $$$${z}=\sqrt{{x}^{\mathrm{2}} +{y}^{\mathrm{2}} } \\ $$

Question Number 74068 Answers: 1 Comments: 4

Question Number 74040 Answers: 1 Comments: 1

Find orthogonal trajectories of the curves: (x−c)^2 +y^2 =c^2 .

$${Find}\:{orthogonal}\:{trajectories}\:{of}\:{the} \\ $$$${curves}:\:\left({x}−{c}\right)^{\mathrm{2}} +{y}^{\mathrm{2}} ={c}^{\mathrm{2}} . \\ $$

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