Hi,(adsbygoogle = window.adsbygoogle || []).push({});

I'm having some trouble with solving this indefinite integral.

[tex]

\int {\sqrt {\frac{{6\cos ^2 x + \sin x\cos (2x) + \sin x}}{{2 - \sin x}}} } dx

[/tex]

I was able to lose the sin(x) and get a cos(x) out of the square root by doing this:

[tex]

\int {\sqrt {\frac{{6\cos ^2 x + \sin x(2\cos^2 x -1) + \sin x}}{{2 - \sin x}}} } dx

[/tex]

[tex]

\int {\sqrt {\frac{{6\cos ^2 x + 2\sin x\cos^2 x -\sin x + \sin x}}{{2 - \sin x}}} } dx

[/tex]

[tex]

\int {\sqrt {\frac{{\cos ^2 x(6 + 2\sin x)}}{{2 - \sin x}}} } dx

[/tex]

[tex]

\int \cos x{\sqrt {\frac{{6 + 2\sin x}}{{2 - \sin x}}} } dx

[/tex]

Then I did a substitution, [tex]y = \sin x \Leftrightarrow dy = \cos xdx[/tex] to get:

[tex]

\int {\sqrt {\frac{{6 + 2y}}{{2 - y}}} } dy

[/tex]

I think I can say this looks a lot better than the initial integral, but after that I used about 3 more substitutions and 2 sides of paper. I finally got something but it wasn't all correct I'm affraid.

I was wondering if I started out wrong or if someone sees an easy way to continue (or an easier to start).

Naughty integral if you ask me

**Physics Forums - The Fusion of Science and Community**

Dismiss Notice

Join Physics Forums Today!

The friendliest, high quality science and math community on the planet! Everyone who loves science is here!

The friendliest, high quality science and math community on the planet! Everyone who loves science is here!

# Goniometric Integral Problem

Loading...

Similar Threads for Goniometric Integral Problem | Date |
---|---|

A Getting a finite result from a non-converging integral | Apr 19, 2018 |

I Decomposing a Certain Exponential Integral | Apr 12, 2018 |

How to make this integral (which does not converge) be finite? | Apr 6, 2018 |

I "Imagine" a definite integral with a finite number of discontinuties | Mar 30, 2018 |

A Maximization problem using Euler Lagrange | Feb 2, 2018 |

**Physics Forums - The Fusion of Science and Community**