Mathematics Stack Exchange is a question and answer site for people studying math at any level and professionals in related fields. Join them; it only takes a minute:

Sign up
Here's how it works:
  1. Anybody can ask a question
  2. Anybody can answer
  3. The best answers are voted up and rise to the top

$$\int\left( {20.56\over x^2-1.27}+x^{55}\right) dx$$

I came to something like this

$$20.56 \int {1\over (x-1)^2 - \frac{27}{100} }~dx + {x^{56}\over56} + \text{Constant}$$

Please can you help me to resolve this?

share|cite|improve this question
up vote 3 down vote accepted

Your integral is of the form $$I = \int \left(\dfrac{a}{x^2 - b^2} + x^n \right)dx$$ Hence, \begin{align} I & = \int \left(\dfrac{a}{2b}\dfrac1{x - b} - \dfrac{a}{2b}\dfrac1{x + b} + x^n \right)dx \\ & = \dfrac{a}{2b} \log(\vert x-b \vert) - \dfrac{a}{2b} \log(\vert x+b \vert) + \dfrac{x^{n+1}}{n+1} + \text{constant}\\ & = \dfrac{a}{2b} \log\left(\left \vert \dfrac{x-b}{x+b} \right \vert \right) + \dfrac{x^{n+1}}{n+1} + \text{constant} \end{align} In your case, $a = 20.56$, $b = \sqrt{1.27}$ and $n = 55$.

share|cite|improve this answer
thanks a lot sir – Sam Dec 16 '12 at 19:21

Your Answer


By posting your answer, you agree to the privacy policy and terms of service.

Not the answer you're looking for? Browse other questions tagged or ask your own question.