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How to calculate the integral below:

$$ \int_{0}^{1}(ax^2+bx+c)^{-3/{2}}dx $$

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    What did you try? Where are you stuck?2011-11-29
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    For $a\ne0$, write $ax^2+bx+c={ a({ (x+{b\over 2a})^2+\underbrace{{c\over a} -{b^2\over 4a^2} }_D) }}$. There are three cases to consider now, depending on whether $D=0$, $D>0$, and $D<0$. Two of these require "inverse trigonometric substitutions". The other leads to a simple integral.2011-11-29
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    I think it would be a good idea if you did some "warm up" problems with $a$, $b$, and $c$ given particular values.2011-11-29
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    @Leaozinho - Okay, then complete the square and try a trigonometric substitution.2011-11-29
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    @Leaozinho - Not getting **what**? Again, try completing the square. If you don't know how to do that, then step away from calculus and learn how to complete the square. Then come back to the problem.2011-11-29
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    @Leaozinho - Okay, so once you complete the square, try a trigonometric substitution in the two cases that David Mitra pointed out in his comment above.2011-11-29

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Hint: Complete the square on $ax^2+bx+c$ and then try a trigonometric substitution. Also, depending on the values of $a$, $b$, and $c$, the integral may be improper (and divergent).

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    @Leaozinho - Complete the square. To be blunt, if you don't know how to do that, then you need to take a step back from calculus and relearn some basic algebraic manipulations.2011-11-29
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    @Leaozinho - 0_o If you don't want to evaluate the integral, then why did you ask how to evaluate it?2011-11-29
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    @Leaozinho - Adding a bunch of exclamation points at the end of your sentences won't endear you to the MSE community. We're not a universal solutions manual that vomits out answers on demand. You have to give us some evidence that you've actually **done some work** before you're likely to get much more help. Once again, try completing the square.2011-11-29
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    @Leaozinho - You've been fairly rude in your comments and questions here in MSE. Your questions come across as barked orders ("Evaluate this integral!!!eleventyones!!1") and you have shown little to no willingness to put forth any effort. Again, we're not here to vomit up answers on demand.2011-11-29