Integrate.    x arcsinx dx

Asked by Harsh | 25th Jul, 2019, 07:02: AM

Expert Answer:

begin mathsize 16px style straight I equals integral xsin to the power of negative 1 end exponent xdx
straight I equals integral sin to the power of negative 1 end exponent straight x space cross times xdx
straight I equals sin to the power of negative 1 end exponent straight x integral xdx minus integral open parentheses fraction numerator dsin to the power of negative 1 end exponent straight x over denominator dx end fraction integral xdx close parentheses dx
straight I equals straight x squared over 2 sin to the power of negative 1 end exponent straight x minus integral fraction numerator 1 over denominator square root of 1 minus straight x squared end root end fraction straight x squared over 2 dx
straight I equals straight x squared over 2 sin to the power of negative 1 end exponent straight x minus 1 half integral fraction numerator straight x squared over denominator square root of 1 minus straight x squared end root end fraction dx
Integrating space further space we space get
straight I equals straight x squared over 2 sin to the power of negative 1 end exponent straight x plus straight x over 4 square root of 1 minus straight x squared end root plus 1 fourth sin to the power of negative 1 end exponent straight x plus straight c end style

Answered by Sneha shidid | 25th Jul, 2019, 09:51: AM

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