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So, from here $$\int \frac{\sin(x)}{3\cos^3(x)+\sin^2(x)\cdot\cos(x)} dx$$ I divided by cos(x) and I got $$\int \frac{\tan(x)}{2\cos^2(x)+1} dx$$ But I'm stuck here. I tried to substitute $t=\cos(x)$

$$\int \frac{-1}{t\cdot(2t^2+1)} dt$$

Any help would be greatly appreciated.

  • 3
    Try $s=t^2$. (And please add $dx$ at the three places where it belongs.)2012-06-13
  • 0
    That is, after the substitution $t=\cos(x)$ that was mentioned in a previous version of the post.2012-06-13
  • 0
    I am inclined to think that the solution I posted below is probably the most straightforward one unless you have one that uses some surprising "trick".2012-06-13

3 Answers 3