# A simple integral - I don't agree with Maple.

## Homework Statement

Evaluate the integral;
$$\int$$2x/(2x+3) dx

## The Attempt at a Solution

Now i start out substituting u=2x+3
Then i get;
$$\int$$2x/u dx

Now i express dx by du;
u=2x+3
du/dx=2x/ln(2)
(du*ln(2))/2x=dx

This expression of dx is inserted into my integral, and the 2^x's cancel out;
$$\int$$2x/u (du*ln(2))/2x
This simplifies to;
$$\int$$ln(2)/u du
Where ln(2) is simply a constant (atleast thats what i think)
so ln(2)$$\int$$1/u
And the integral becomes;
ln(2)*ln(u)

Substituting back into the integral;

ln(2)*ln(2x+3)

Now maple didn't give me this result. Instead it gave me the following;
ln(2x+3)/ln(2)

Any idea of what i've done wrong ? :P

I would recheck your du/dx calculation.

D H
Staff Emeritus
Any idea of what i've done wrong ? :P

u=2x+3
du/dx=2x/ln(2)
Try doing that derivative again.

dextercioby
$$\int \frac{2^x}{2^{x} +3}{}dx= \int \frac{e^{(\ln 2) x}}{e^{(\ln 2)x} +3} dx =...$$