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

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6-7

Definite Integrals of Special Functions

6.1 Elliptic Integrals and Functions

Notation: k=1k2si1_e(cf.8.1).

6.11 Forms containing F (x, k)

6.111

0π/2F(x,k)cotxdx=π4K(k)+12lnkK(k)

si2_e  BI (350)(1)

6.112

1. 

0π/2F(x,k)sinxcosx1+ksin2xdx=14kK(k)ln(1+k)k2+π16kK(k)

si3_e  BI (350)(6)

2. 

0π/2F(x,k)sinxcosx1ksin2xdx=14kK(k)ln2(1k)kπ16kK(k)

si4_e  BI (350)(7) ...

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