## anonymous 4 years ago Indefinite Integral Help int (x/(2x+1) dx I keep getting (x/2)-((1/4)ln|2x+1|)+1/4+C Book says ((1/2)x)-((1/4)ln|2x+1|)+C. So when I get a constant as part of the answer when trying to find the indefinite integral, do I just consider it as part of the constant C? Is that why I'm off by +1/4?

1. TuringTest

yes, 1/4 is absorbed into C, because C is unknown that will happen a lot in differential equations, so get used to it

2. Akshay_Budhkar

yes whenever you have another constant, you ought to add it into C. The C absorbs it.. If you are having marks for steps then this step will count for marks as well ( maybe 1/2 mark or so if u r scoring full elsewhere)

3. TuringTest

wolfram keeps the 1 though ironically http://www.wolframalpha.com/input/?i=int%20(x%2F(2x%2B1)%20dx&t=crmtb01 but they left it in the parentheses, so I guess they feel it's justified

4. Akshay_Budhkar

but in the alternate forms it does absorb the constant :D

5. TuringTest

right^

6. Akshay_Budhkar

turing i need u 1 min

7. Akshay_Budhkar

i will give u the link

8. Akshay_Budhkar
9. TuringTest

I don't even see why they add the 1 for 'restricted values of x' in wolf what does that mean, do you know akshay?

10. myininaya

what are you guys doing?

11. myininaya

12. myininaya

13. TuringTest

yes, but why does wolf add the 1 for 'restricted values' I want to know

14. myininaya

$\int\limits_{}^{}\frac{x}{2x+1} dx$ u=2x+1 => du=2 dx u=2x+1 => (u-1)/2=x $\int\limits_{}^{}x \cdot \frac{1}{2x+1} dx=\int\limits_{}^{}\frac{u-1}{2} \cdot \frac{1}{u} \frac{du}{2}$ $\frac{1}{4}\int\limits_{}^{}\frac{u-1}{u} du=\frac{1}{4}\int\limits_{}^{}(1-\frac{1}{u}) du=\frac{1}{4}(u-\ln|u|)+C$

15. myininaya

$=\frac{1}{4}(2x+1-\ln|2x+1|)+C$

16. myininaya

$=\frac{x}{2}+\frac{1}{4}-\frac{1}{4} \ln|2x+1| +C$

17. myininaya

$=\frac{x}{2}-\frac{1}{4}\ln|2x+1|+c$

18. myininaya

i will look at wolfram's solution one sec

19. myininaya

No I don't know what they are talking about honestly lol

20. myininaya

either one of those things they have listed is fine though

21. myininaya

imperialist seems smart I will ask him what he think wolfram means