MATHEMATICAL FORMULA AND ELLIPTIC FUNCTIONS 



7.172 



. cl 



:. I * sm - = c. 

 L #J 



;. til - cos - ) = o. 8. sin- log (a + be x ) 



L \ %l Joo X Joo 



cv 2 "i 



i) 



6. 



7.173 



sm- 



i. 



[sin x\ 

 = I- 

 * Jo 



ftan o:l 



2. = I. 



L * Jo 



Ksin nx\ m ~{ 

 ) 1= nm ' 



7.174 



. X + l>lSX \ = e b. 



4. 



=o 



5- [log cos x - cot s]o = o. 



fco/ 



' _ 



. * . 



II 



Kc cVl 



cos - +. a sin - 

 X X] Jo 



4. [sin" 1 x - cot #] = i. 



[f /7T X\ ) coix ~\ 

 i tan (4 + l) 



P X - T l 



7. - = i. 



L * Jo 



8. [# log #] = o 



[e x e~ x 2x~\ _ i 

 (^-i) 3 Jo " 3' 



10. 



II. 





6. Flog tan g + *) cot J = i. I2 . p^JELHl . ,. 

 L U 2/ Jo L log tan x Jo 



