Question

Find the following integral

Answer 1

what is the integer?

Answer 2

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

Answer 3

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

Answer 4

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) ?

Answer 5

yea i think it does lol

Answer 6

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

Answer 7

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