I`m trying to integrate the following: $$\int\frac{2\cdot \cos^2(x)}{x^2}dx$$ what I did first is: $$\int \frac{2\cdot (\frac{1}{2}+\frac{cos2x}{2})}{x^2}dx=\int \frac{1+cos2x}{x^2}dx$$ now what? any suggestions? thanks!
Asked
Active
Viewed 71 times
2
-
Do you mean $\cos^2 x$ instead of $\cos x^2$? – njguliyev Oct 28 '13 at 22:56
-
I changed it. thanks. – Ofir Attia Oct 28 '13 at 22:57
-
You will not be able to express this integral in terms of the elementary functions. – njguliyev Oct 28 '13 at 23:02
1 Answers
1
Using a simple integration by parts, we arrive at the following expression, which, as has already mentioned above, is irreducible to elementary functions: $$F(x)=-2\left[\frac{\cos^2x}x+\text{Si}(2x)\right]$$ where $\text{Si}(t)=\int\frac{\sin x}x dx$.
Lucian
- 48,334
- 2
- 83
- 154