## souvik one year ago integration

1. souvik

$\int\limits_{}^{}\sqrt{\tan x} ~~dx$

2. anonymous

Make a substitution $t^2 = tanx$

3. anonymous

$x = \tan^{-1} t^2$ can you do the rest?

4. souvik

i found$\int\limits_{}^{}\frac{ 2t^2 }{ 1+t^4 }dt$ now?

5. anonymous

$\int\limits \frac{ 2t^2 }{ 1+t^4 }dt \implies \int\limits \frac{ t^2+1+t^2-1 }{ t^4+1 } dt = \int\limits \frac{ t^2+1 }{ t^4+1 }dt + \int\limits \frac{ t^2-1 }{ t^4+1 }$

6. anonymous

you'll have to do the integrals separately now

7. souvik

how?

8. anonymous

$\int\limits \frac{ t^2+1 }{ t^2+1 } dt \implies \int\limits \frac{ 1+1/t^2 }{ t^2+1/t^2 } dt$ now do another u substation do so similarly with other integral.

9. souvik

$\int\limits_{}^{}\frac{ 1-1/t^2 }{t^2+1/t^2 }$

10. anonymous

Let u = t-1/t^2 for the first integral and similarly you would let u = t+1/t for the second integral (the one you presented)