Math Help - Why is my evaluation of this integral wrong?

1. Why is my evaluation of this integral wrong?

My work is attached and any input would be greatly appreciated!

2. algebra, algebra, algebra ...

$u^2+25 \ne (u-5)(u+5)$

$\int \frac{e^{4x}}{e^{8x} + 25} \, dx
$

$u =e^{4x}$

$du = 4e^{4x} \, dx$

$\frac{1}{4} \int \frac{4e^{4x}}{e^{8x} + 25} \, dx$

$\frac{1}{4} \int \frac{du}{u^2 + 25} \, dx$

$\frac{1}{20} \arctan\left(\frac{u}{5}\right) + C
$

$\frac{1}{20} \arctan\left(\frac{e^{4x}}{5}\right) + C$

3. Originally Posted by skeeter
algebra, algebra, algebra ...

$u^2+25 \ne (u-5)(u+5)$

$\int \frac{e^{4x}}{e^{8x} + 25} \, dx
$

$u =e^{4x}$

$du = 4e^{4x} \, dx$

$\frac{1}{4} \int \frac{4e^{4x}}{e^{8x} + 25} \, dx$

$\frac{1}{4} \int \frac{du}{u^2 + 25} \, dx$

$\frac{1}{20} \arctan\left(\frac{u}{5}\right) + C
$

$\frac{1}{20} \arctan\left(\frac{e^{4x}}{5}\right) + C$
How on god's green earth could you read that sheet!? :0

4. Originally Posted by AllanCuz
How on god's green earth could you read that sheet!? :0
I decipher hieroglyphs in my spare time ...

5. Oh ya! I always make that mistake when I do things fast. Thanks! (and lol sorry for my handwriting)