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problem on integration using adjustment

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evaluate integral of  x / (x+1)^2
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adjust the expression x in the numerator
according to the denominator, by adding and
subtracting 1, then divide term by term, simplify
and then integrate
answer and  some steps are given below
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other examples:
evaluate integral of { e^(1 /x^2)} / {x^3} -------------(integration by substitution)
integral of ( ( 4 - x^2 )^( 3/2) ) with limits 0 to 1--------------integration by substitution




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