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(x)/((x+1)(x+2)) |
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Answer» Solution :` int (x)/((x+1)(x+2)) DX =I (" say ")` ` " LET " (x)/((x+1)(x+2)) =(A)/((x+1))+(B)/((x+2))` `RARR (x)/((x+1)(x+2))=(A(x+2)+B(x+1))/((x+1)(x+2))` ` rArrx=A (x+2)+B(x+1)` `rArr x=-1 " then "-1= A(-1+2)+0` `A=-1` `rArr x=-2 " then "-2=0 +B (-1)` `B=2` `:. I = int (x)/((x+1)(x+2))dx ` `= int ((-1))/(x+1)dx+ int (2)/(x+2)dx` `=- LOG (x+1) +2 log (x+2)+c` ` =- log (x+1)+log (x+2)^(2)+c` ltb rgt `=log |(x+2)^(2)/(x+1)|+c` |
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