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.

Before I ask my next question, I think this is a great forum, and wish I could know more about the collective people who post here (types of careers that use math? grad students?

What are your non-Math interests? Is there an "Off-topic" subforum on StackExchange? I'd love to know what else you guys engage with in life...and what else interests you folks...or what your non-work/math goals in life are)

Another big thanks to people who help others here. I can't say it enough.

Anyways...How do I begin integrating this one? $$\int_0^x\frac{1}{1-t-t^2}dt$$

I don't think this is a u/du substitution. Do I change it to this? $$\int_0^x (1-t-t^2)^{-1} dt=$$

Disclaimer: I am not a student posting his homework assignment. I am an adult learning Calculus.

share|improve this question
    
Hint: Complete the square. –  Amzoti Dec 6 '13 at 13:54
    
Substitute $u = \left(t+\frac12\right)$. You get $\int_{1/2}^{x+1/2} \frac{du}{5/4 - u^2}$, which you probably know how to handle. Or do a partial fraction decomposition. –  Daniel Fischer Dec 6 '13 at 13:54
    
Look in your textbook for "partial fractions" .... there may be a section called "integrating rational functions" but maybe only stuck in the middle of "methods of integration". –  GEdgar Dec 6 '13 at 14:29
    
Ok, so the bottom line is this is an advanced integration technique that I have yet to encounter? I will look it up, or revisit at a later date. Thanks! –  JackOfAll Dec 6 '13 at 22:51
    
Not sure where to go from here: $$\int_0^x\frac{1}{\frac{5}{4}-u^2}du$$ Also not sure how to change limits of integration. What topic should I look up, in order how to do this? I have not encountered this method when learning basic u/du substitution for indefinite integrals –  JackOfAll Dec 8 '13 at 17:31

1 Answer 1

up vote 1 down vote accepted

Hint: Write the integrand as $\dfrac{1}{5/4- (t+1/2)^2}$

share|improve this answer
    
Are there poles within the integration interval? –  Ron Gordon Dec 6 '13 at 15:33
    
Depends on the value of $x$. –  LTS Dec 6 '13 at 16:38
    
Ok, so the bottom line is this is an advanced integration technique that I have yet to encounter? I will look it up, or revisit at a later date. Thanks! –  JackOfAll Dec 6 '13 at 22:51
    
No, actually it is not advanced at all. I have just completed the square, now you just need to substitute $u=t + 1/2$ and split into partial fractions, then you can integrate. You will need to use $\int \frac{1}{x} \mathrm{d}x = \ln{x}+C$ –  LTS Dec 6 '13 at 23:30
    
Not sure where to go from here: $$\int_0^x\frac{1}{\frac{5}{4}-u^2}du$$ Also not sure how to change limits of integration. What topic should I look up, in order how to do this? I have not encountered this method when learning basic u/du substitution for indefinite integrals –  JackOfAll Dec 8 '13 at 17:29

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.