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Table of Integrals, Series, and Products, 8th Edition by Daniel Zwillinger

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0π/2ln?(1k2sin2x)dx1k2sin2x=ln?k'?K(k)

si1244_e  BI (323)(1)

2. 

0π/2ln(1k2sin2x)sin2x?dx1k2sin2x=1k2{(k22+ln?k')K(k)+(2ln?k')E(k)}

si1245_e  BI (323)(3)

3.12 

0π/2ln(1k2sin2x)cos2x?dx1k2sin2x=1k2[(1+k'2k'2ln?k')K(k)(2ln?k')E(k)]

si1246_e  BI (323)(6)

4. 

π/20ln(1k2sin2x)?dx(1k2sin2x)3=1k'2[(k22)K(k)(2+ln?k')E(k)]

si1247_e  BI (323)(9)

5.12 

0π/2ln(1

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