Please reply showing your steps, so we can try to help you find any errors. Thank you!
Hello!
I have tried to solve these two integrals, but I get the wrong answer.
The first one is 4/x^2 - 4 (upper limit is 1, lower limit 0).
The correct answer is -ln2, but I get 2arctan(x/2) + c.
The next one is ln^2 x/2x (upper limit e^2, lower limit 1).
I am not sure what the correct answer is, but either
a) 4/3 b) 1/4 c) 3/5 d) 7/6 e) 4/9
I would appreciate your help,
best wishes
Amine
It will be much easier to adress your troubles and misconceptions (and you have several of each) if you post all your work. Also, it would help if your equations were less ambiguous. I assume by 4/x^2 - 4 you mean 4/(x^2 - 4) and by ln^2 x/2x you mean (ln^2 x)/(2x) ....
I presume you mean 4/(x^2-4), not (4/x^2)- 4. "arctan" is the integral of dx/(x^2+1), not dx/(x^2-4). To integrate that, write 1/(x^2-4) as 1/((x-2)(x+2)) and use "partial fractions". That is, find A and B such that 4/(x^2- 4)= A/(x-2)+ B(x+2) and integrate those separately.
Use the simple substitution u= ln(x).The next one is ln^2 x/2x (upper limit e^2, lower limit 1).
I am not sure what the correct answer is, but either
a) 4/3 b) 1/4 c) 3/5 d) 7/6 e) 4/9
I would appreciate your help,
best wishes
Amine