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How can I calculate $$ \int{\sec\left(x\right)\tan\left(x\right) \over 3x + 5}\,{\rm d}x $$

My Try:: $\displaystyle \int \frac{1}{3x+5}\left(\sec x\tan x \right)\,\mathrm dx$

Now Using Integration by Parts::

We Get $\displaystyle = \frac{1}{3x+5}\sec x +\int \frac{3}{(3x+5)^2}\sec x\,\mathrm dx$

Now My Question is How Can I calculate (II) Integral.

Please explain this to me.


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In mathematics, it is not necessary to use a dot . to indicate product; if you really want an explicit indication of it, then the TeX command \cdot will provide you with a centred dot: $\cdot$. –  Lord_Farin May 18 '13 at 8:04
Mathematica refuses symbolic integration. Did the original problem include bounds on your integral (making it a definite integral instead of an indefinite one)? –  Lord_Farin May 18 '13 at 8:13
I don't think that's going to come out to be doable with elementary functions with that linear term in the denominator and something trigonometric in the numerator. Also, I think your derivative is slightly off. –  Mike May 18 '13 at 8:15
I agree with Mike. No this is not going to be able to...it seems that you will have infinite terms integrating symbolically –  Keith Afas Aug 4 '13 at 0:27
If you convert the secant into a power series, then you may be able to write an expression for the integral. –  john doe Sep 24 '13 at 6:52

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