integration by substitution: e^(2x)/(4 + (e^4x))

[icyhot2590]

e^(2x)/(4 + (e^4x))

i know that the formula is du/a^2+u^2 = 1/a arctan u/a +c

a=2
u=e^x2

after that im stuck please help

 

[galactus]

Let's do it form scratch.

Let \(\displaystyle \L\\u=e^{2x}, \;\ du=2e^{2x}dx, \;\ \frac{du}{2}=e^{2x}dx\)

This gives:

\(\displaystyle \L\\\frac{1}{2}\int\frac{1}{4+u^{2}}du\)

Now, you're on your way.

 

[icyhot2590]

ok thanks so....

a=2
u=u

1/2 arctanu/2 +c

1/4 arctan u/2 +c

is that right

 

[galactus]

u=e^(2x)

 

[icyhot2590]

1/4 arctan e^2x/2 +c

 

[skeeter]

check for yourself if you integrated correctly ... take the derivative of your solution and see if it matches the integrand of your original integral.