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IntegrationQuestion and Answers: Page 1
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Question and Answers Forum |
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IntegrationQuestion and Answers: Page 1 |
| I_n =∫_0 ^( 1) ∫_0 ^1 ...∫_0 ^( 1) (((x_1 x_2 ...x_n )^a )/((1−x_1 x_2 ...x_n )))ln(x_(1 ) )ln(x_2 )...ln(x_(n ) )dx_1 dx_2 ...dx_(n ) |
| I_n = ∫_0 ^( 1) ∫_0 ^( 1) ....∫_0 ^( 1) ((ln(1+x_1 x_2 ....x_n ))/((1−x_1 )(1−x_2 )....(1−x_(n ) ))) dx_1 dx_2 ....dx_n |
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| ∫_( 0) ^( 1) ((1+x−x^2 +x^3 −x^4 −x^5 )/(1−x^7 )) dx |
| ∫^( ∞) _( 0) ((10x^(17) e^(2x) (e^(2x) −1)+x^(17) e^x (e^(4x) −1))/((e^x −1)^6 )) dx |
| Q. Integrate ((x^2 +x+1)/(2x^2 −x−3)). |
| I = ∫^( 16) _( 1) (((x +(√x))^(1/4) )/x^(3/4) ) dx |
| ∫ ((e^(−x^2 ) cos (x))/(x^2 +1)) dx |
| ∫_1 ^( 2) ∫_1 ^( 2) ∫_1 ^( 2) ∫_1 ^( 2) x_1 ^( 2) x_2 ^( 3) x_3 ^( 4) x_4 ^( 5) dx_1 dx_2 dx_3 dx_(4 ) |
| ∫_1 ^( 3) ∫_1 ^( 3) ∫_1 ^( 3) ∫_1 ^( 3) ∫_1 ^( 3) ((x_1 +x_2 +x_3 +x_4 −x_5 )/(x_1 +x_2 +x_3 +x_4 +x_5 )) dx_1 dx_2 dx_3 dx_4 dx_5 |
| ∫_1 ^( 2) ∫_1 ^( 2) ∫_1 ^( 2) ∫_1 ^( 2) ((x_1 +x_(2 ) +x_3 −x_4 )/(x_1 +x_2 +x_3 +x_4 )) dx_1 dx_2 dx_3 dx_(4 ) |
| L{sinx}=∫_0 ^∞ e^(−sx) sinx dx=∫_0 ^∞ e^(−sx) ((e^(ix) −e^(−ix) )/(2i))dx =(1/(2i))[∫_0 ^∞ e^(−(s−i)x) dx −∫_0 ^∞ e^(−(s+i)x) dx] =(1/(2i))[((−1)/(s−i))e^(−(s−i)x) +(1/(s+i))e^(−(s+i)x) ]_0 ^∞ =(1/(2i))[(1/(s−i))−(1/(s+i))]=(1/(2i))×((s+i−s+i)/((s−i)(s+i)))=(1/(2i))×((2i)/(s^2 +1))=(1/(s^2 +1)) |
| Lim_(x→∞) Σ_(i=1) ^∞ (((−x)/i))^i |
| ∫tan(((1/n)/(sec(n)+(((1−sec(n))/(sec(n))))))dn |
| I=∫tan(((cos(n))/(n(1−cos(n) + cos^2 (n))))) dn |
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| a , b, ∈ R ∫_( −∞) ^( ∞) (((e^(iax) −1)(e^(ibx) −1))/x^2 ) dx |
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| Prove; ∫^( ∞) _( 0) (1/(2^2^(⌊x⌋) + {x})) dx = ln2 |
| Prove; I_0 (x) =(1/π)∫_0 ^( π) e^( x cox(θ)) dθ ; x^2 I_0 ^(′′) (x) + xI′_0 (x) − x^2 I_0 (x) = 0; |
| f(x,y)=ln∫_0 ^(x^2 +y^2 ) e^t^2 dt,f(x)(1,2)=? |
| f(t) = (1/(2πi)) ∫_( c−i∞) ^( c+i∞) (e^(st) /(s^k )) ds , k ∈C |
| f(t)=∫_(0 ) ^( t) ((ζ(1/2 + iτ))/( (√(t − τ + 1)))) dτ |
| ∫(√((x+1)/(x+2))) .(1/(x+3)) dx=? |