Integral

Calculus (Integrals, Series)
Post Reply
User avatar
Riemann
Posts: 176
Joined: Sat Nov 14, 2015 6:32 am
Location: Melbourne, Australia

Integral

#1

Post by Riemann »

Let $a\geq 1$. Prove that:

$$\int_{0}^{\pi} \left ( 1 + \cos x \right ) \ln \left ( a + \cos x \right )\, \mathrm{d}x = \pi \left ( a - \sqrt{a^2-1} \right ) + \pi \ln \left ( \frac{a + \sqrt{a^2-1}}{2} \right )$$
$\displaystyle \sum_{n=1}^{\infty}\frac{1}{n^s}= \prod_{p \; \text{prime}}\frac{1}{1-p^{-s}}$

Tags:
Post Reply

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

Register

Sign in

Who is online

Users browsing this forum: No registered users and 7 guests