EXAMPLES XI 



171 



3 



4- 18 cosh- 1 



6 , , x - 8\ . 



cosh- 1 ;-- ! -i- 5 y#2 _ fa + Q 



a;- 8 



10 cosh- 1 j + (x - 3 + 5) Vx 2 -Gx+6 



x 8 

 = 10 cosh- 1 7= + te + 2)Vx 2 - Ox + 6 



Vs 



The result can also be expressed as 



(2# 2 - 7x + 10) da; ra? - 3 + Vx 2 - Ox + 



f(2# 2 - 7x + 10) da; r 



\ - . == - = 10 lOg, < 



J Vx* - 6x + 6 



6x + 6 



+ (x + 2) Vx* Ox + 6 



EXAMPLES XI 



Solve the following integrals : 



(1) Jvf^P 



(3) U/9-ir 2 dx 



w f,* 8 



J VOx -x 2 

 (7) f V&x - x 2 dx 



f dx 



(9) . 



J V9 + 8x - x 2 



(11) JV9+ %x-x 2 dx 



(13) f y rfa? 



J VlO + Gx - 3x 2 



(15) I VlO + 6x - 3x 2 dx 



C 



(17) -7- 

 Jva; 



2) dx 



w f 



f(3a; 2 - 7x + 3) da 



(4) I . 



V 9 # 2 



f(to-l)dc 



I \ /fi 2 



(8) 1^ + ^-^ 

 (10) J'^-^'^ 



>f>2 _, K\ /7-r> 



rftC Jj '/,/ 



(12) 



<U) f-,11 



Jvio 



\/9 



(4 - 5x) dx 



+ 6x - 3x 2 

 (5x 2 + 12) dr 



c 2 +25 

 (19) JVa; 2 + 25 dx 



