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Mathematics 7 Online
OpenStudy (anonymous):

Integrate (sqrt(1 + x^2)/x)

OpenStudy (anonymous):

\[x = \tan \theta dx = \sec^2 \theta \]

OpenStudy (anonymous):

I think I need a simpler route with the trig substitution.... the way I tried was lasting almost two pages....

hartnn (hartnn):

yes, that substitution is correct, so what did u get in terms of theta ?

OpenStudy (anonymous):

It's the substituting it into the equation, then simplifying that I experienced trouble with.

hartnn (hartnn):

1+tan^2 theta = ? sec theta* coas theta = ?

hartnn (hartnn):

*cos

hartnn (hartnn):

u get sec theta * sec^2 theta / tan theta , right ?

OpenStudy (anonymous):

yeah

hartnn (hartnn):

so what is sec theta / tan theta ?? and write sec^2 theta as 1+ tan^2 theta

hartnn (hartnn):

u will get , csc t (1+sec^2 t) = csc t +csc t .sec^2 t =csc t+ tan t sec t integrate these seperately, these are standard integrals. then resubstitute for t

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