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IntegrationQuestion and Answers: Page 159

Question Number 99114    Answers: 1   Comments: 0

calculate: ∫(√x)sinh^(−1) (x)dx where sinh^(−1) (x) is the inverse hyperbolic sine function

calculate:xsinh1(x)dxwheresinh1(x)istheinversehyperbolicsinefunction

Question Number 99044    Answers: 3   Comments: 0

∫(1/(x^2 +1))dx=?

1x2+1dx=?

Question Number 99007    Answers: 2   Comments: 0

Let I_y = ∫_(−2) ^2 [y^3 cos ((y/2)) + (1/2)]((√(4−y^2 )) ) dy then I_y = ???

LetIy=22[y3cos(y2)+12](4y2)dythenIy=???

Question Number 98951    Answers: 0   Comments: 1

∫tan^(1/5) x.cotx.secxdx

tan15x.cotx.secxdx

Question Number 98944    Answers: 1   Comments: 0

let g(x) =((cosx +1)/(cos(2x)−3)) developp f at fourier serie

letg(x)=cosx+1cos(2x)3developpfatfourierserie

Question Number 98942    Answers: 3   Comments: 2

calculate ∫ ((x+1−(√(2x+3)))/(x−2 +(√(x+1)))) dx

calculatex+12x+3x2+x+1dx

Question Number 98929    Answers: 0   Comments: 6

Find[]the[]integral[]of[] ∫(dt/(√((1+t^(10) ))))

Find[]the[]integral[]of[]dt(1+t10)

Question Number 99173    Answers: 1   Comments: 0

Question Number 98885    Answers: 0   Comments: 2

find the range f(x)=log_4 log_2 log_(1/2) (x)

findtherangef(x)=log4log2log12(x)

Question Number 98884    Answers: 2   Comments: 0

calculate ∫_0 ^∞ ((lnx)/((x+1)^4 ))dx

calculate0lnx(x+1)4dx

Question Number 98883    Answers: 1   Comments: 0

calculate ∫_0 ^∞ (dx/(x^8 +x^4 +1))

calculate0dxx8+x4+1

Question Number 98831    Answers: 1   Comments: 1

Question Number 98826    Answers: 0   Comments: 2

Given ∫_0 ^∞ (dx/(a^2 +x^2 )) = (π/(2a)) find ∫_0 ^∞ (dx/((a^2 +x^2 )^3 )) ?

Given0dxa2+x2=π2afind0dx(a2+x2)3?

Question Number 98821    Answers: 1   Comments: 0

∫ _0 ^∞ (dx/(a^2 +x^2 )) = ?

0dxa2+x2=?

Question Number 98776    Answers: 0   Comments: 0

∫_0 ^∞ (((x−1))/(ln(F(x)(√5)+cos(πx)(ϕ)^(−x) −1)(√(F(x)(√5)+cos(πx)(ϕ)^(−x) −1))))dx F(x)=Fib(x)=xth Extended fibonacci number f:R→R ϕ=((1+(√5))/2)

0(x1)ln(F(x)5+cos(πx)(φ)x1)F(x)5+cos(πx)(φ)x1dxF(x)=Fib(x)=xthExtendedfibonaccinumberf:RRφ=1+52

Question Number 98744    Answers: 0   Comments: 2

∫_0 ^π ∫_0 ^(2sinθ) (1+rsinθ)r dr dθ

0π02sinθ(1+rsinθ)rdrdθ

Question Number 98722    Answers: 3   Comments: 0

let f(x) =arctan((3/x)) 1) calculste f^((n)) (x) and f^((n)) (1) 2) developp f at integr seri at point x_0 =1

letf(x)=arctan(3x)1)calculstef(n)(x)andf(n)(1)2)developpfatintegrseriatpointx0=1

Question Number 98721    Answers: 2   Comments: 0

calculate ∫_0 ^∞ (dx/(x^4 +x^2 +1)) 1) by using residue theorem 2) by using complex decomposition

calculate0dxx4+x2+11)byusingresiduetheorem2)byusingcomplexdecomposition

Question Number 98713    Answers: 2   Comments: 1

∫((sin(x))/x)dx

sin(x)xdx

Question Number 98679    Answers: 1   Comments: 2

prove that ∫_0 ^∞ ((3+2(√x))/(x^2 +2x+5))dx=4.13049

provethat03+2xx2+2x+5dx=4.13049

Question Number 98672    Answers: 1   Comments: 0

∫_0 ^4 ∫_0 ^(x/4) e^x^2 dx dy

040x4ex2dxdy

Question Number 98623    Answers: 3   Comments: 0

evaluate ∫_(2/(√3)) ^2 (1/(x^2 (√(4+x^2 ))))dx using the substitution x=2tanθ

evaluate2321x24+x2dxusingthesubstitutionx=2tanθ

Question Number 98594    Answers: 1   Comments: 0

Question Number 98589    Answers: 1   Comments: 0

calculate ∫_0 ^∞ ((sin(αx^2 ))/(x^2 +4))dx with α real

calculate0sin(αx2)x2+4dxwithαreal

Question Number 98588    Answers: 0   Comments: 0

calculate ∫_(−∞) ^∞ ((xsin(x))/((x^2 +x+1)^2 ))dx

calculatexsin(x)(x2+x+1)2dx

Question Number 98587    Answers: 1   Comments: 0

calculate ∫_(−∞) ^(+∞) ((cos(αx))/(x^4 +1))dx (α real)

calculate+cos(αx)x4+1dx(αreal)

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