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Question Number 72665    Answers: 1   Comments: 5

∫_( 2) ^( 3) ((tan^(−1) (x))/(1 − x^2 )) dx

$$\int_{\:\mathrm{2}} ^{\:\mathrm{3}} \:\:\frac{\mathrm{tan}^{−\mathrm{1}} \left(\mathrm{x}\right)}{\mathrm{1}\:−\:\mathrm{x}^{\mathrm{2}} }\:\mathrm{dx} \\ $$

Question Number 72641    Answers: 0   Comments: 2

Question Number 72494    Answers: 1   Comments: 1

((∫x(√(x^2 +5)) dx−3∫(x/(√(x^2 +5)))dx)/(∫((x(x^2 +2))/(√(x^2 +5))) dx))

$$\frac{\int{x}\sqrt{{x}^{\mathrm{2}} +\mathrm{5}}\:{dx}−\mathrm{3}\int\frac{{x}}{\sqrt{{x}^{\mathrm{2}} +\mathrm{5}}}{dx}}{\int\frac{{x}\left({x}^{\mathrm{2}} +\mathrm{2}\right)}{\sqrt{{x}^{\mathrm{2}} +\mathrm{5}}}\:{dx}} \\ $$

Question Number 72466    Answers: 1   Comments: 2

Prove that ∫_0 ^( 2) ∫_(−(√(1−(y−1)^2 ))) ^( 0 ) xy^2 dxdy = −(4/5) after changing the integral to polar form.

$${Prove}\:{that}\:\int_{\mathrm{0}} ^{\:\mathrm{2}} \int_{−\sqrt{\mathrm{1}−\left({y}−\mathrm{1}\right)^{\mathrm{2}} }} ^{\:\:\mathrm{0}\:} \:{xy}^{\mathrm{2}} {dxdy}\:=\:−\frac{\mathrm{4}}{\mathrm{5}} \\ $$$$\boldsymbol{{after}}\:\mathrm{changing}\:\mathrm{the}\:\mathrm{integral}\:\mathrm{to}\:\boldsymbol{\mathrm{polar}}\:\boldsymbol{\mathrm{form}}. \\ $$

Question Number 72445    Answers: 0   Comments: 0

∫((x cos(ax))/(1+x^2 )) dx

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

Question Number 72401    Answers: 1   Comments: 0

Find the area bounded by one leaf of the rose r = 12cos (3θ).

$${Find}\:{the}\:{area}\:{bounded}\:{by}\:{one}\:{leaf}\:{of} \\ $$$${the}\:{rose}\:{r}\:=\:\mathrm{12cos}\:\left(\mathrm{3}\theta\right). \\ $$

Question Number 72397    Answers: 0   Comments: 4

find A(x)=∫_0 ^(π/2) ln(1−xsin^2 θ)dθ with ∣x∣<1

$${find}\:{A}\left({x}\right)=\int_{\mathrm{0}} ^{\frac{\pi}{\mathrm{2}}} {ln}\left(\mathrm{1}−{xsin}^{\mathrm{2}} \theta\right){d}\theta\:\:\:{with}\:\mid{x}\mid<\mathrm{1} \\ $$

Question Number 72396    Answers: 0   Comments: 2

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

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

Question Number 72392    Answers: 0   Comments: 1

calculate A_n =∫_0 ^∞ e^(−nx) ln(1+x)dx with n natural ≥1

$${calculate}\:{A}_{{n}} =\int_{\mathrm{0}} ^{\infty} \:{e}^{−{nx}} {ln}\left(\mathrm{1}+{x}\right){dx}\:\:{with}\:{n}\:{natural}\:\geqslant\mathrm{1} \\ $$

Question Number 72391    Answers: 0   Comments: 1

calculte ∫_0 ^∞ (((−1)^([x]) )/(4+x^2 ))dx

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

Question Number 72346    Answers: 0   Comments: 1

Question Number 72337    Answers: 1   Comments: 1

Evaluate ∫_(−5) ^5 ((√(25−x^2 )) ) dx using ⇒ an algebraic method ⇒ Geometrical mehod thanks in advanced great mathematicians

$${Evaluate}\:\:\int_{−\mathrm{5}} ^{\mathrm{5}} \left(\sqrt{\mathrm{25}−{x}^{\mathrm{2}} }\:\right)\:{dx}\:{using} \\ $$$$\Rightarrow\:{an}\:{algebraic}\:{method} \\ $$$$\Rightarrow\:{Geometrical}\:{mehod}\: \\ $$$${thanks}\:{in}\:{advanced}\:{great}\:{mathematicians} \\ $$

Question Number 72336    Answers: 0   Comments: 0

Obain an equation for ⇒ the left Reimen Sum ⇒ the right Reimen sum ⇒ Trapeziodal rule ⇒ Newton Raphson′s Iteration Hence find and approximate value for ∫_0 ^3 (e^x + x^2 )dx

$${Obain}\:{an}\:{equation}\:{for}\: \\ $$$$\Rightarrow\:{the}\:{left}\:{Reimen}\:{Sum} \\ $$$$\Rightarrow\:{the}\:{right}\:{Reimen}\:{sum} \\ $$$$\Rightarrow\:{Trapeziodal}\:{rule} \\ $$$$\Rightarrow\:{Newton}\:{Raphson}'{s}\:{Iteration} \\ $$$$\:\:{Hence}\:{find}\:{and}\:{approximate}\:{value}\:{for}\:\int_{\mathrm{0}} ^{\mathrm{3}} \left({e}^{{x}} \:+\:{x}^{\mathrm{2}} \right){dx} \\ $$

Question Number 72359    Answers: 1   Comments: 2

Question Number 72259    Answers: 1   Comments: 0

∫yz dx +∫xz dy +∫xy dz pleas sir help me ?

$$\int{yz}\:{dx}\:+\int{xz}\:{dy}\:+\int{xy}\:{dz}\:\:\:\:{pleas}\:{sir}\:{help}\:{me}\:? \\ $$

Question Number 72286    Answers: 0   Comments: 0

Question Number 72287    Answers: 0   Comments: 0

Question Number 72390    Answers: 0   Comments: 1

calculate U_n =∫_0 ^∞ ((arctan(1+x^4 ))/((x^2 +n^2 )^3 ))dx and determine nature of the serie Σ U_n

$${calculate}\:{U}_{{n}} =\int_{\mathrm{0}} ^{\infty} \:\:\frac{{arctan}\left(\mathrm{1}+{x}^{\mathrm{4}} \right)}{\left({x}^{\mathrm{2}} \:+{n}^{\mathrm{2}} \right)^{\mathrm{3}} }{dx} \\ $$$${and}\:{determine}\:{nature}\:{of}\:{the}\:{serie}\:\Sigma\:{U}_{{n}} \\ $$

Question Number 72060    Answers: 0   Comments: 2

∫((sin x)/(1+sin x+sin 2x))dx=?

$$\int\frac{\mathrm{sin}\:{x}}{\mathrm{1}+\mathrm{sin}\:{x}+\mathrm{sin}\:\mathrm{2}{x}}{dx}=? \\ $$

Question Number 72025    Answers: 1   Comments: 1

calculate ∫_0 ^∞ e^(−αx) ln(x)dx with α>0

$${calculate}\:\:\int_{\mathrm{0}} ^{\infty} \:{e}^{−\alpha{x}} {ln}\left({x}\right){dx}\:\:{with}\:\alpha>\mathrm{0} \\ $$

Question Number 72017    Answers: 0   Comments: 0

find ∫ ((x+(√(4+x^2 )))/(x−(√(4+3x^2 ))))dx

$${find}\:\int\:\:\frac{{x}+\sqrt{\mathrm{4}+{x}^{\mathrm{2}} }}{{x}−\sqrt{\mathrm{4}+\mathrm{3}{x}^{\mathrm{2}} }}{dx} \\ $$

Question Number 72016    Answers: 1   Comments: 2

find U_n =∫_0 ^∞ ((cos(nx))/((3+nx^2 )^2 ))dx with n integr

$${find}\:{U}_{{n}} =\int_{\mathrm{0}} ^{\infty} \:\:\:\frac{{cos}\left({nx}\right)}{\left(\mathrm{3}+{nx}^{\mathrm{2}} \right)^{\mathrm{2}} }{dx}\:\:{with}\:{n}\:{integr} \\ $$

Question Number 72015    Answers: 0   Comments: 1

find ∫ ((arctan(x−(1/x)))/(x^2 +1))dx

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

Question Number 72012    Answers: 0   Comments: 1

find f(α) =∫_0 ^∞ ((arctan(αx))/((x^2 +3)^2 ))dx with α real.

$${find}\:{f}\left(\alpha\right)\:=\int_{\mathrm{0}} ^{\infty} \:\:\frac{{arctan}\left(\alpha{x}\right)}{\left({x}^{\mathrm{2}} +\mathrm{3}\right)^{\mathrm{2}} }{dx}\:\:{with}\:\alpha\:{real}. \\ $$

Question Number 72011    Answers: 1   Comments: 1

calculate ∫_0 ^∞ ((ln(3+x^2 ))/((x^2 +1)^2 ))dx

$${calculate}\:\int_{\mathrm{0}} ^{\infty} \:\:\frac{{ln}\left(\mathrm{3}+{x}^{\mathrm{2}} \right)}{\left({x}^{\mathrm{2}} +\mathrm{1}\right)^{\mathrm{2}} }{dx} \\ $$

Question Number 71921    Answers: 0   Comments: 0

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