Advertisements
Advertisements
Question
Find `int (x + 1)/(x(1 - 2x)) dx`.
Sum
Advertisements
Solution
`int (x + 1)/(x(1 - 2x)) dx = int x/(x(1 - 2x)) dx + int 1/(x(1 - 2x)) dx`
⇒ `int (x + 1)/(x(1 - 2x)) dx = int 1/((1 - 2x)) dx + int 1/x dx + int 2/((1 - 2x)) dx`
⇒ `int (x + 1)/(x(1 - 2x)) dx = - 1/2 log |1 - 2x| + log |x| - 2 xx 1/2 log |1 - 2x| + C`
⇒ `int (x + 1)/(x(1 - 2x)) dx = - 3/2 log |1 - 2x| + log |x| + C`
shaalaa.com
Is there an error in this question or solution?
