$\displaystyle \int \sqrt {\frac{1}{t^{2}}+4+4t^{2}}dt $ apparently reduces to $\displaystyle \int( \frac{1}{t}+2t)dt $ how is this possible? I tried simplifying and stuff but no result on my end...
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Realize that $\displaystyle 4t^4+4t^2+1=(2t^2+1)^2$. Roy
Originally Posted by akhayoon $\displaystyle \int \sqrt {\frac{1}{t^{2}}+4+4t^{2}}dt $ apparently reduces to $\displaystyle \int( \frac{1}{t}+2t)dt $ how is this possible? I tried simplifying and stuff but no result on my end... $\displaystyle \frac 1{t^2} + 4 + 4t^2 = \frac 1{t^2} (1 + 4t^2 + 4t^4)$ ...........now factorzie $\displaystyle = \frac 1{t^2}(2t^2 + 1)^2$ i think you can take it from here
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