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IntegrationQuestion and Answers: Page 149

Question Number 105951    Answers: 2   Comments: 0

Question Number 105940    Answers: 1   Comments: 0

∫_0 ^1 log(tanθ)dθ

01log(tanθ)dθ

Question Number 105862    Answers: 3   Comments: 1

∫ (dx/(9+16cos^2 x)) ?

dx9+16cos2x?

Question Number 105815    Answers: 1   Comments: 0

Question Number 105781    Answers: 1   Comments: 1

Please, I need help. Exercise We have : J_n = ∫_0 ^( (π/4)) tan^n (x) dx 1) Establish a recurrence relation between J_(n+2) and J_n . 2) Calculate J_0 and J_1 , then deduce the expression of J_n as a function of n. The deduction of the last question, please.

Please,Ineedhelp.ExerciseWehave:Jn=0π4tann(x)dx1)EstablisharecurrencerelationbetweenJn+2andJn.2)CalculateJ0andJ1,thendeducetheexpressionofJnasafunctionofn.Thedeductionofthelastquestion,please.

Question Number 105755    Answers: 2   Comments: 0

∫ (dx/(√(x(√x) −x^2 ))) ?

dxxxx2?

Question Number 105753    Answers: 1   Comments: 1

∫ ((x^2 +sin^2 x)/(x^2 +cos^2 x)) dx

x2+sin2xx2+cos2xdx

Question Number 105743    Answers: 1   Comments: 1

Question Number 105722    Answers: 4   Comments: 1

∫ (√(x−(√x))) dx

xxdx

Question Number 105700    Answers: 1   Comments: 0

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

ππx2dx1+sin(sinx)+1+sin2(sinx)

Question Number 105673    Answers: 2   Comments: 0

Question Number 105574    Answers: 1   Comments: 0

∫ ((x−1)/(x+x^2 ln x)) dx ?

x1x+x2lnxdx?

Question Number 105565    Answers: 1   Comments: 0

let f(x) =x^2 ln(1−x^3 ) 1) calculate f^((n)) (x) and f^((n)) (0) 2) developp f at integr serie 3)calculate ∫ f(x)dx

letf(x)=x2ln(1x3)1)calculatef(n)(x)andf(n)(0)2)developpfatintegrserie3)calculatef(x)dx

Question Number 105471    Answers: 0   Comments: 2

Σ_(k=1) ^n ((1/k))^2

nk=1(1k)2

Question Number 105455    Answers: 3   Comments: 0

∫_(−1) ^1 ((e^x −e^(−x) )/(cos x)) dx

11exexcosxdx

Question Number 105440    Answers: 1   Comments: 3

∫tanx∙tan2x∙tan3x∙dx Any way to solve this without the use of partial fractions?

tanxtan2xtan3xdxAnywaytosolvethiswithouttheuseofpartialfractions?

Question Number 105412    Answers: 2   Comments: 0

∫_0 ^(π/2) ln (cos x) dx

π/20ln(cosx)dx

Question Number 105411    Answers: 1   Comments: 0

∫((x^2 +3)/(x^6 (x^2 +1)))dx Is there any special method of decomposition other than the use of partial fractions ?

x2+3x6(x2+1)dxIsthereanyspecialmethodofdecompositionotherthantheuseofpartialfractions?

Question Number 105399    Answers: 0   Comments: 0

calculate ∫_(−∞) ^(+∞) ((x^2 dx)/((x^2 +x+1)^2 (2x^2 +3)))

calculate+x2dx(x2+x+1)2(2x2+3)

Question Number 105393    Answers: 1   Comments: 0

∫_(−π) ^π ((x sin x dx)/((1+x+(√(1+x^2 )))(√(3+sin^2 x))))

ππxsinxdx(1+x+1+x2)3+sin2x

Question Number 105386    Answers: 2   Comments: 0

∫ (x^3 /(√((a^2 +x^2 )^3 ))) dx

x3(a2+x2)3dx

Question Number 105353    Answers: 0   Comments: 0

solve y^(′′ ) +2y^′ −y =x^n e^(−x) n integr natural

solvey+2yy=xnexnintegrnatural

Question Number 105233    Answers: 0   Comments: 0

calculate ∫_0 ^∞ ((ch(cosx)−cos(chx))/(x^2 +3))dx

calculate0ch(cosx)cos(chx)x2+3dx

Question Number 105232    Answers: 1   Comments: 0

calculate ∫_0 ^∞ ((cos(2x^2 ))/((4x^2 +9)^3 ))dx

calculate0cos(2x2)(4x2+9)3dx

Question Number 105231    Answers: 1   Comments: 0

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

calculate0+2x21(x2+x+1)2(x2x+1)2dx

Question Number 105230    Answers: 2   Comments: 0

calculate ∫_1 ^(+∞) (dx/((x^2 +1)^2 (x^2 +4)^2 ))

calculate1+dx(x2+1)2(x2+4)2

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