Logarithmic and Trigonometric Integral
Logarithmic and Trigonometric Integral
$$\int^{\frac{\pi}{6}}_{0}\ln^2(2\sin x)dx$$
Re: Logarithmic and Trigonometric Integral
A hint is along these lines. Apply the sub $x=\arctan t$ and use the well known fact that
$$\sin \left ( \arctan t \right ) = \frac{t}{\sqrt{t^2+1}}$$
The final answer is $\dfrac{7 \pi^3}{216}$.
$$\sin \left ( \arctan t \right ) = \frac{t}{\sqrt{t^2+1}}$$
The final answer is $\dfrac{7 \pi^3}{216}$.
$\displaystyle \sum_{n=1}^{\infty}\frac{1}{n^s}= \prod_{p \; \text{prime}}\frac{1}{1-p^{-s}}$
Re: Logarithmic and Trigonometric Integral
Thanks Riemann answer is Right. would you like to explain me in detail.
Create an account or sign in to join the discussion
You need to be a member in order to post a reply
Create an account
Not a member? register to join our community
Members can start their own topics & subscribe to topics
It’s free and only takes a minute
Sign in
Who is online
Users browsing this forum: No registered users and 1 guest