Question

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?

Answer 1

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

Answer 2

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)

Answer 3

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

Answer 4

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

Answer 5

right^

Answer 6

turing i need u 1 min

Answer 7

i will give u the link

Answer 8

http://openstudy.com/study#/updates/4f14d598e4b0b9109c920bca

Answer 9

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?

Answer 10

what are you guys doing?

Answer 11

comparing your answers with wolfram?

Answer 12

sprusty 1/4+constant is still a constant
so your answer and the book answer are fine! :)

Answer 13

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

Answer 14

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

Answer 15

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

Answer 16

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

Answer 17

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

Answer 18

i will look at wolfram's solution one sec

Answer 19

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

Answer 20

either one of those things they have listed is fine though

Answer 21

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