How can I calculate $\int \frac{\sec x\tan x}{3x+5}\,\mathrm dx$

Asked May 18 '13 at 07:58

Active Oct 01 '18 at 03:57

Viewed 1,273 times

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.

edited Oct 01 '18 at 03:57

Archer

asked May 18 '13 at 07:58

juantheron

4

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 08:04
3

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 08:13
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 08:15
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 04 '13 at 00:27
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 06:52
Too much computation time on Wolfram. Guessing it's not really possible or REALLY long. – Shahar Dec 15 '13 at 22:28
This has no closed form solution according to integrals.wolfram – Hakim Jun 24 '14 at 18:35
@juantheron May I ask the source of this problem pelase? – Ahaan S. Rungta Aug 28 '14 at 21:10
See this thread. – Ahaan S. Rungta Aug 28 '14 at 21:10

0 Answers0