## KatClaire 2 years ago Find the following integral

1. kugler97

what is the integer?

2. KatClaire

$\int\limits_{}^{} \frac{ (2t+1)^{2} }{ \sqrt{t} } dt$

3. KatClaire

does $\frac{ t ^{2} }{ \sqrt{t} }$ cancel out????

u need to expand of (2t + 1)^2 = 4t^2 + 4t + 1 and convert sqrt(t) = t^(1/2) now, can u simplify (4t^2 + 4t + 1)/t^(1/2) ?

5. kugler97

yea i think it does lol

6. KatClaire

well I'll show you how far I got $4 \int\limits_{}^{} \frac{ t ^{2} }{ t ^{1/2} } +4 \int\limits_{}^{} \frac{ t }{ t ^{1/2} } + \int\limits_{}^{} \frac{ 1 }{ t ^{1/2} }$

so far is good, then use the properties of exponent to simplify of them : |dw:1358987039172:dw|

now, what would be ur integral ?

9. KatClaire

Sorry openstudy crapped out last night lol thanks

nopes.. :) btw, do u got it ?

11. KatClaire

Mhmm :) I got $\frac{ 8t ^{^{5/2}} }{ 5 }+\frac{ 8t ^{3/2} }{ 3 }+ 2t ^{1/2}+c$ Look about right?

yeah, i have cheked ur answer you are right :)

13. KatClaire

Hehe you are the best thanks!!!!