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Question

x sin1x dx=
  1. (x2214)sin1x+x41x2+c
  2. (x22+14)sin1x+x41x2+c
  3. (x2214)sin1xx41x2+c
  4. (x22+14)sin1xx41x2+c


Solution

The correct option is A (x2214)sin1x+x41x2+c
x sin1x dx=x22sin1x11x2.x22dx+c=x22sin1x12(1x2)11x2dx+c=x22sin1x+121x2dx1211x2dx+c=x22sin1x+x41x2+14sin1x12sin1x+c=x22sin1x+x41x214sin1x=(x2214)sin1x+x41x2+c

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