What is the problem here I get diffrent result ....
$\displaystyle \int_0^2 \frac{\frac{5}{2}}{4x^4+25}= \frac{5}{2}\int_0^2 \frac{1}{(2x^2)^2+5^2}dx = \frac{5*1}{2*5} arctan (\frac{2x^2}{5}) $
What is the problem here I get diffrent result ....
$\displaystyle \int_0^2 \frac{\frac{5}{2}}{4x^4+25}= \frac{5}{2}\int_0^2 \frac{1}{(2x^2)^2+5^2}dx = \frac{5*1}{2*5} arctan (\frac{2x^2}{5}) $
I think you mean $\displaystyle \frac{1}{(2x^2)^2+5^2}$ not $\displaystyle {1}{(2x^2)^2+5^2}$
Look to this formula carefaully (Assuming a dont equal 0):
$\displaystyle \int \frac{1}{x^2 + a^2} dx = \frac{1}{a} arctan \frac{x}{a} + C$
Are you sure your problem is similar to it?
i.e. when you substituting $\displaystyle u=2x^2$ , You will get your du in the numerator?
You forgot the $\displaystyle dx$ in the first integral. Also its a definite integral, Its result must be a number not a function.
Oh sorry I didn't notice. I found it now here
http://www.mathhelpforum.com/math-he...rp-8-11-a.html