I'm having trouble integrating (100+2t)^3/2.
I get [5(100+2t)^5/2]/5/2, which I think should be simplified to just 2(100+2t)^5/2. But the answer is just (100+2t)^5/2. What am I doing wrong?

Question

I'm having trouble integrating (100+2t)^3/2. 
I get [5(100+2t)^5/2]/5/2, which I think should be simplified to just 2(100+2t)^5/2. But the answer is just (100+2t)^5/2. What am I doing wrong?

ganeshie8 · Answer

you may use wolfram to verify : http://www.wolframalpha.com/input/?i=%5Cint+%28100%2B2t%29%5E%283%2F2%29+dt

anonymous · Answer

yeah wolfram alpha shows me the right answer but it doesn't show me how it got to that answer.

anonymous · Answer

I'm not sure what step I am not doing, or doing incorrectly.

ganeshie8 · Answer

$$\large \int (100+2t)^{\frac{3}{2}} ~dt$$


substitute $u = 100+2t$
$du =  2dt  $

$dt = \dfrac{du}{2}$

ganeshie8 · Answer

the integral becomes :
$$\large  \int   u^{\frac{3}{2}} \frac{du}{2}$$

ganeshie8 · Answer

$$\large \frac{1}{2}\int  u^{\frac{3}{2}}~dt$$

ganeshie8 · Answer

integrate ^^