ex-int-indef - Exercise Indenite Integrals 1 ShowZthat(a(3...

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Exercise °Inde±nite Integrals 1. Show that (a) Z (3 ° x 2 ) 3 dx = 27 x ° 9 x 3 + 9 5 x 5 ° 1 7 x 7 + C (b) Z ° 1 ° 1 x 2 ± q x p xdx = 4( x 2 + 7) 7 4 p x + C (c) Z ° a x + a 2 x 2 + a 3 x 3 ± dx = a ln j x j ° a 2 x ° a 3 2 x 2 + C (d) Z x + 1 p x dx = 2 3 x p x + 2 p x + C (e) Z (1 ° x )(1 ° 2 x )(1 ° 3 x ) dx = x ° 3 x 2 + 11 3 x 3 ° 3 2 x 4 + C (f) Z x 2 1 + x 2 dx = x ° tan ° 1 x + C (g) Z (1 + sin x + cos x ) dx = x ° cos x + sin x + C (h) Z 5 p 1 ° 2 x + x 2 1 ° x dx = ° 5 2 5 p (1 ° x ) 2 + C (i) Z (2 x + 3 x ) 2 dx = 4 x ln 4 + 2 6 x ln 6 + 9 x ln 9 + C (j) Z (2 x ° 3) 10 dx = 1 22 (2 x ° 3) 11 + C (k) Z dx 1 + cos x = tan x= 2 + C (l) Z xdx p 1 ° x 2 = ° p 1 ° x 2 + C (m) Z xdx (1 + x 2 ) 2 = ° 1 2(1 + x 2 ) + C (n) Z dx p x (1 + x ) = 2 tan ° 1 p x + C (o) Z dx p x (1 ° x ) = 2 sin ° 1 p x + C (p) Z xe ° x 2 dx = ° 1 2 e ° x 2 + C (q) Z dx p 1 + e 2 x = ° ln ² e ° x + p 1 + e ° 2 x ³ + C (r) Z dx e x + e ° x = tan ° 1 e x + C (s) Z ln 2 x x dx = 1 3 ln 3 x + C (t) Z dx x ln x ln(ln x ) = ln j ln j ln x jj + C (u) Z sin 5 x cos xdx = 1 6 sin 6 x + C (v) Z sin x + cos x 3 p sin x ° cos x dx = 3 2 3 p 1 ° sin 2 x + C (w) Z x (1 ° x ) 100 dx = 1 99(1 ° x ) 99 ° 1
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