i would like these all solved correctly.

1 6. Consider the inte ral I = dz: g / V3 2m 11:2 (3) Use the technique of "completing the square" to write this in the form 1 I = f'/a2(1:+b)2 d3" (b) Now use the substitution 1:. : 1: + b to find the integral. 7. Use integration by parts to find: (a) fare3 [11: (b) [1:2 ln(:c) d1: (c) [as cos(:c)d:c 1 8. Evaluate the integral / tcosh(t) dt. 0 9. Harder: Use integration by parts to find (a) flnmdx (b) [sin\"(r)dw (c) janmnzda: 10. (3) Use integration by parts to show that cos(:c) sin("'1)(3:) [sin"(m) d1: = i (117:1) jsin"2(m)d1:. n (b) Use the reduction formula in (a) and the trig. identity c0522: = 1 sin2$ to find / sin2 :1: c032 :r: clan . (This technique is useful when the powers are even.) (c) Use the result in (a) to find f2 sin4mdm. 0