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x2  x Q.23 Evaluate: (ex  x 1)2 dx x(x  1) e2xx(x 1) [Sol. I =  e2x (1 xex  ex )2 dx =  1 (x 1)e x 2 dx put (x + 1)e–x = t  [– (x + 1)e–x + e–x] dx = dt  e–x(–x) dx = dt t(dt) t dt 1 t 1  dt 1  I =  (1 t)2 = –  (1 t)2 = –  (1 t)2 dt = –   (1 t)   (1 t)2 dt  1 = C – ln (1 + t) – 1 t = C – ln(1 + (x + 1)e–x) – 1 1 (x 1)ex   Ans.] Q.30 Integrate : x2 (x cos x  sin x)(x sin x  c

Author

Raju Singh

Language

EN