fall02 Integration problems from old exams - Mat104 Fall 2002 Integration Problems From Old Exams Compute the following integrals sin5 x dx cos x sin 1

# Thomas' Calculus: Early Transcendentals

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Mat104 Fall 2002, Integration Problems From Old Exams Compute the following integrals (1) sin 5 x cos x dx (2) dx (4 + x 2 ) 5 / 2 (3) sin( 1 + x ) dx (4) arctan( x ) dx (5) cos 4 x dx (6) π/ 2 0 cos x 4 - sin 2 x dx (7) ln(1 + ln x ) x dx (8) x 2 arctan x dx (9) 2 - 1 dx (4 + 2 x + x 2 ) 5 / 2 (10) x sin( x 2 ) e x 2 dx (11) dx x 2 + 25 (12) 2 + x 3 x + 2 + x dx (13) 3 x 2 x 2 + x - 2 dx (14) cos 3 x 3 x dx (15) dx x 2 + 2 x (16) x 2 + 3 x - 3 ( x + 1)( x 2 + 6 x + 10) dx (17) dx x 1 - x 2 (18) x 3 e x 2 dx (19) x 2 ln x dx (20) x 3 1 - x 2 dx (21) tan 4 θ dθ (22) x + 1 x 2 + 4 x + 13 dx (23) π/ 2 0 cos x sin 2 x + 5 sin x + 6 dx (24) e x/ 2 1 + e x dx (25) 2 x 2 + 5 x + 10 x 3 + 2 x 2 + 10 x dx (26) ( x - 2) 9 - x 2 dx (27) e 1 arcsin(ln x ) x dx (28) 1 0 xe - x dx 1
2 (29) (ln x ) 2 dx (30) sin x 1 + cos x dx (31) x 2 x 6 - 1 dx (Hint: Try a substitution first.) (32) sin 5 x cos 2 x dx