split the fraction so ( x/(2x+1) -1/(2x + 1))dx
now let u= 2x + 1
x =(u -1)/2
integrate separately using the above substitution on the first piece
the second is just -1/u integrated
*her ^^'but i can't understand the last two steps in his solution how 2/(2x+1) become (2x+1) ???
Do you know the integration/derivative rules? If not, you should first learn them.
Their answer is the correct one. If that's all you wanted to know, you could have used WolframAlpha.