- #1

Levis2

- 43

- 0

## Homework Statement

Evaluate the integral;

[tex]\int[/tex]2

^{x}/(2

^{x}+3) dx

## The Attempt at a Solution

Now i start out substituting u=2

^{x}+3

Then i get;

[tex]\int[/tex]2

^{x}/u dx

Now i express dx by du;

u=2

^{x}+3

du/dx=2

^{x}/ln(2)

(du*ln(2))/2

^{x}=dx

This expression of dx is inserted into my integral, and the 2^x's cancel out;

[tex]\int[/tex]2

^{x}/u (du*ln(2))/2

^{x}

This simplifies to;

[tex]\int[/tex]ln(2)/u du

Where ln(2) is simply a constant (atleast thats what i think)

so ln(2)[tex]\int[/tex]1/u

And the integral becomes;

ln(2)*ln(u)

Substituting back into the integral;

ln(2)*ln(2

^{x}+3)

Now maple didn't give me this result. Instead it gave me the following;

ln(2

^{x}+3)/ln(2)

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