Take the 2-minute tour ×
Mathematics Stack Exchange is a question and answer site for people studying math at any level and professionals in related fields. It's 100% free, no registration required.

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

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|improve this question
add comment

1 Answer

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

Your Answer

 
discard

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.