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Expert: Robi Bhattacharjee - 9/20/2008


Question
Integral of (x^2-1)/(x^2-16)

Answer
Hello Danusha,

Thanks for this question! Calculus is one of my all-time favorite subjects and I always find a nice question interesting.

This is a pretty interesting integral.

To do this problem, you just do (x^2 - 1)/(x^2 - 16) = (x^2 - 16 + 15)/
(x^2 - 16).

Then you can use the distributive property to get = (x^2 - 16)/(x^2 - 16) + 15/(x^2 - 16) = 1 + 15/(x^2-16). Now to integrate this I will use a formula that is easily derivable from partial fractions. SO it =

x + 15/8 *ln(x-4) - 15/8 *ln(x+4) + C.

so basically, the trick is to separate the numerator into the denominator + a constant.



I hope this helped,

Robi  

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Robi Bhattacharjee

Expertise

I can answer a variety of questions on mathematics. Questions on trigonometry, calculus(preferably single variable), algebra, geometry, and number theory will be answered. I cannot answer questions on abstract branches of mathematics such as group theory. I also cannot answer questions on statistics. In number theory, I can answer questions on congruences, prime numbers, units, functions, and the riemann-zeta function.

Experience

I have studied advanced math my entire life. I started calculus in sixth grade. I have attended numerous math competitions and I am attending math organizations such as the San-Diego math circle. Also, this year I have been invited to the USAMO which is a prestigious math competition (Every year the USAMO invites 500 students from across the USA to participate in this competition. The top 6 go to represent the USA in the International Math Olympiad).

Organizations
I am in the San Diego Math Circle

Education/Credentials
I am entering high school and have received a perfect score and the STAR test 5 times in a row. I also have gotten recognitions in the AMC 10, AIME, Math Counts, and ARML. Additionally, I have won the San Diego Math Olimpiad twice in a row.

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