# Math Help - integral

1. ## integral

$\int \sqrt {\frac{1}{t^{2}}+4+4t^{2}}dt$

apparently reduces to $\int( \frac{1}{t}+2t)dt$

how is this possible? I tried simplifying and stuff but no result on my end...

2. Realize that $4t^4+4t^2+1=(2t^2+1)^2$.

Roy

3. Originally Posted by akhayoon
$\int \sqrt {\frac{1}{t^{2}}+4+4t^{2}}dt$

apparently reduces to $\int( \frac{1}{t}+2t)dt$

how is this possible? I tried simplifying and stuff but no result on my end...
$\frac 1{t^2} + 4 + 4t^2 = \frac 1{t^2} (1 + 4t^2 + 4t^4)$ ...........now factorzie

$= \frac 1{t^2}(2t^2 + 1)^2$

i think you can take it from here