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IntegrationQuestion and Answers: Page 1

Question Number 209923 Answers: 0 Comments: 0

Solve: ∫((sin(x!))/(x!))dx

$$\boldsymbol{{Solve}}:\:\int\frac{\boldsymbol{{sin}}\left(\boldsymbol{{x}}!\right)}{\boldsymbol{{x}}!}\boldsymbol{{dx}} \\ $$

Question Number 209800 Answers: 1 Comments: 1

Question Number 209773 Answers: 0 Comments: 0

Question Number 209691 Answers: 0 Comments: 0

∫(2x^(3x^2 +4x−7) )(log _2 (x^2 +3x−7))e^(x^2 +3x−5) dx=?

$$\:\:\:\int\left(\mathrm{2x}^{\mathrm{3x}^{\mathrm{2}} +\mathrm{4x}−\mathrm{7}} \right)\left(\mathrm{log}\:_{\mathrm{2}} \:\left(\mathrm{x}^{\mathrm{2}} +\mathrm{3x}−\mathrm{7}\right)\right)\mathrm{e}^{\mathrm{x}^{\mathrm{2}} +\mathrm{3x}−\mathrm{5}} \:\mathrm{dx}=? \\ $$

Question Number 209687 Answers: 3 Comments: 0

Question Number 209685 Answers: 1 Comments: 0

Question Number 209662 Answers: 1 Comments: 0

∫(1/(sin^2 x(1+cos^2 x)))dx

$$\int\frac{\mathrm{1}}{\mathrm{sin}^{\mathrm{2}} {x}\left(\mathrm{1}+\mathrm{cos}^{\mathrm{2}} {x}\right)}{dx} \\ $$

Question Number 209557 Answers: 2 Comments: 0

Given ∫_2 ^4 (ax^n +1)dx=58 ∫_0 ^2 (ax^n +1)dx=10 find the value of a and n

$${Given}\: \\ $$$$\:\int_{\mathrm{2}} ^{\mathrm{4}} \left({ax}^{{n}} +\mathrm{1}\right){dx}=\mathrm{58}\:\:\:\:\:\int_{\mathrm{0}} ^{\mathrm{2}} \left({ax}^{{n}} +\mathrm{1}\right){dx}=\mathrm{10} \\ $$$${find}\:{the}\:{value}\:{of}\:\:{a}\:\:\:{and}\:\:{n} \\ $$

Question Number 209544 Answers: 1 Comments: 0

∫_0 ^4 (dx/(∣x−1∣+∣x−2∣+∣x−4∣))

$$\:\:\:\:\:\: \\ $$$$\:\:\:\:\:\:\:\:\:\:\:\:\:\:\int_{\mathrm{0}} ^{\mathrm{4}} \frac{{dx}}{\mid{x}−\mathrm{1}\mid+\mid{x}−\mathrm{2}\mid+\mid{x}−\mathrm{4}\mid} \\ $$$$ \\ $$

Question Number 209543 Answers: 1 Comments: 2

∫(dx/(x^4 +4))

$$\:\: \\ $$$$\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\int\frac{{dx}}{{x}^{\mathrm{4}} +\mathrm{4}} \\ $$$$ \\ $$

Question Number 209484 Answers: 0 Comments: 0

∫_e^x ^e^2 ((1/(2+ln t)) )dt =?

$$\:\:\:\:\:\:\:\underset{\mathrm{e}^{\mathrm{x}} } {\overset{\mathrm{e}^{\mathrm{2}} } {\int}}\:\left(\frac{\mathrm{1}}{\mathrm{2}+\mathrm{ln}\:\mathrm{t}}\:\right)\mathrm{dt}\:=? \\ $$

Question Number 209393 Answers: 1 Comments: 3

∫_0 ^(π/2) ((ln(tanx))/(1+tanx))dx

$$\int_{\mathrm{0}} ^{\frac{\pi}{\mathrm{2}}} \frac{{ln}\left({tanx}\right)}{\mathrm{1}+{tanx}}{dx} \\ $$

Question Number 209353 Answers: 1 Comments: 0

Question Number 209332 Answers: 3 Comments: 0

Question Number 209217 Answers: 2 Comments: 0

calculate : I= ∫_(0 ) ^( ∞) (( tan^( −1) (x))/((1 + x^( 2) )^( 2) )) dx = ?

$$ \\ $$$$\:\:\:\:\:\:\:\:\:\:\:\:\boldsymbol{{calculate}}\:: \\ $$$$\:\:\:\: \\ $$$$\:\:\:\:\:\:\:\:\:\:\:\mathrm{I}=\:\int_{\mathrm{0}\:} ^{\:\infty} \frac{\:{tan}^{\:−\mathrm{1}} \left({x}\right)}{\left(\mathrm{1}\:+\:{x}^{\:\mathrm{2}} \right)^{\:\mathrm{2}} }\:{dx}\:=\:?\:\:\:\:\: \\ $$$$ \\ $$

Question Number 208900 Answers: 0 Comments: 0

Does anyone know of an intuition behind the integral form of the remainder in Taylor′s theorem?

$${Does}\:{anyone}\:{know}\:{of}\:{an}\:{intuition} \\ $$$${behind}\:{the}\:{integral}\:{form}\:{of}\:{the} \\ $$$${remainder}\:{in}\:{Taylor}'{s}\:{theorem}? \\ $$

Question Number 208871 Answers: 3 Comments: 0

L=∫_0 ^1 (√((4−3x)/(4+5x)))dx

$${L}=\int_{\mathrm{0}} ^{\mathrm{1}} \sqrt{\frac{\mathrm{4}−\mathrm{3}{x}}{\mathrm{4}+\mathrm{5}{x}}}{dx} \\ $$

Question Number 208842 Answers: 1 Comments: 1

does the rule of odd and even functions can be applied with improper integration? I=∫_(−∞) ^∞ xe^(−x^2 ) dx while f(x)= xe^(−x^2 ) is odd then I =0

$${does}\:{the}\:{rule}\:{of}\:{odd}\:{and}\:{even}\:{functions}\: \\ $$$${can}\:{be}\:{applied}\:{with}\:{improper}\:{integration}? \\ $$$${I}=\int_{−\infty} ^{\infty} {xe}^{−{x}^{\mathrm{2}} } {dx}\: \\ $$$${while}\:\:{f}\left({x}\right)=\:{xe}^{−{x}^{\mathrm{2}} } \:{is}\:{odd} \\ $$$${then}\:{I}\:=\mathrm{0} \\ $$

Question Number 208805 Answers: 0 Comments: 3

Integrate: (xdz − zdx) − a^2 (2xzdz − z^2 dx) + 2x^3 = 0

$$\mathrm{Integrate}: \\ $$$$\left(\mathrm{xdz}\:−\:\mathrm{zdx}\right)\:−\:\mathrm{a}^{\mathrm{2}} \left(\mathrm{2xzdz}\:−\:\mathrm{z}^{\mathrm{2}} \mathrm{dx}\right)\:+\:\mathrm{2x}^{\mathrm{3}} \:=\:\mathrm{0} \\ $$

Question Number 208791 Answers: 0 Comments: 1

If ∫ (dx/(x^3 (1 + x^6 )^(2/3) )) = xf(x).(1 + x^6 )^(1/3) + C where C is constant of integration then find f(x).

$$\mathrm{If}\:\int\:\frac{{dx}}{{x}^{\mathrm{3}} \left(\mathrm{1}\:+\:{x}^{\mathrm{6}} \right)^{\frac{\mathrm{2}}{\mathrm{3}}} }\:=\:{xf}\left({x}\right).\left(\mathrm{1}\:+\:{x}^{\mathrm{6}} \right)^{\frac{\mathrm{1}}{\mathrm{3}}} \:+\:{C}\: \\ $$$$\mathrm{where}\:{C}\:\mathrm{is}\:\mathrm{constant}\:\mathrm{of}\:\mathrm{integration}\:\mathrm{then} \\ $$$$\mathrm{find}\:{f}\left({x}\right). \\ $$

Question Number 208733 Answers: 1 Comments: 0

2∫_(1/3) ^1 ((x(√(−3x^2 +4x−1)))/(7x^2 −4x+1))dx=? Exact solution needed.

$$\mathrm{2}\underset{\frac{\mathrm{1}}{\mathrm{3}}} {\overset{\mathrm{1}} {\int}}\frac{{x}\sqrt{−\mathrm{3}{x}^{\mathrm{2}} +\mathrm{4}{x}−\mathrm{1}}}{\mathrm{7}{x}^{\mathrm{2}} −\mathrm{4}{x}+\mathrm{1}}{dx}=? \\ $$$$\mathrm{Exact}\:\mathrm{solution}\:\mathrm{needed}. \\ $$

Question Number 208692 Answers: 1 Comments: 0

∫_0 ^(π/2) xln sin x dx=?

$$\underset{\mathrm{0}} {\overset{\pi/\mathrm{2}} {\int}}{x}\mathrm{ln}\:\mathrm{sin}\:{x}\:{dx}=? \\ $$

Question Number 208661 Answers: 1 Comments: 0

⇃

$$\:\:\downharpoonleft\underline{\:} \\ $$

Question Number 208652 Answers: 1 Comments: 0

Question Number 209957 Answers: 0 Comments: 0

If x, y are contain in natural numbers and x² + y² = 613² Find the values of x + y = ?

Question Number 208632 Answers: 1 Comments: 1

∫e^(−x^2 ) dx could this be integrated by part? What approach would most likely be suitable for this integral?

$$\int{e}^{−{x}^{\mathrm{2}} } {dx} \\ $$$${could}\:{this}\:{be}\:{integrated}\:{by}\:{part}?\:{What} \\ $$$${approach}\:{would}\:{most}\:{likely}\:{be}\:{suitable} \\ $$$${for}\:{this}\:{integral}? \\ $$$$ \\ $$

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