Question

1. Compute the following integrals. (a) [6pts] | Vi Ina de (b) (ópts/ tan” x sec x dx dx (0) [10pts) / vz2+1 х 5.x2 - x + 2 (a) [10pts] / dx x3 + x (e) [6pts] dx 1 (6) (6pts | e-</2 dx

Answer 1

(a) Se loge de = Sxle logndu By Appling By Part het uus asste consider logn as Frent function - log nan 3½ مهابه 31 I du 3 n us & loga nih / Sah dx !! 2 log regel 3 312 4 n tc 9 (b). S to tan a see redu - Put tant n = Seen -1 Shree x-1) tann benda Put been=u bee hann du= du n - S (u² - 1) du seen عام - U seen tan'n been dna her's secuto Is to 3

In JH²+1 du u= 1 + x² du= (1 +4 29 12 du = 1 an du niti elu dn 2 du uz 4²_1 u ²1 f S والے u²1 2 -se Stus + du 1) de Si olan bir ²-2² log/ H-1 7+ f u + c ga M+1 J I +6² AC log | JT 4112 Si to? + e x + 2 S 5x² x2 + x alr

11 5 x² - + 2 dn xor+1) 9-62 Nc4+1) s) du du-2 SU Side -SE S 3-) MCH+1) du By Partial fraction = 5n 4 RtI - 72 dn 11 5x +2(4 log (x+1) log(x)) + C 52 +8 log (4+1) + a log ntl, = 57-8 log IC & +1) 1 + 2 log/2) + C, Start 2 (x-11'ls de 2 AIS -576x139 5 L 4