Indefinate integration problems

  • Thread starter Thread starter JakePearson
  • Start date Start date
  • Tags Tags
    Integration
JakePearson
Messages
52
Reaction score
0
Indefinate integration problems!

find the following indefinate integrals?

d) ∫ 6x2 / sqrt(2x3 + 9)
e) ∫ x sqrt(1 - x2
f) ∫ 4 / (x + 2)(x + 3)

can you help me answer these please
 
Physics news on Phys.org


You keep posting questions with absolutely no work or ideas. Please post what you've tried, what techniques do you know, what is causing the problem, etc. Review u-substitution in your book, and then post again if you are still stuck. I've seen multiple posts on homework type questions. Whether it's for a class or not, you aren't getting what you need to out of the exercises if you are posting nearly every question and not struggling through it yourself. I'm not trying to be difficult, but I'm trying to force you to try.

Try something! If it doesn't work, then why didn't it work? How can you modify it? These are techniques you have to learn so that you aren't reliant on others to complete your work.
 


Substitution is a good method to try. Another thing that works well for anti derivatives is to try a function that you think may work, differentiate it, and see what you can add to it (constants, etc) to get the desired result. After doing this a while you'll build up your intuition.
 
Prove $$\int\limits_0^{\sqrt2/4}\frac{1}{\sqrt{x-x^2}}\arcsin\sqrt{\frac{(x-1)\left(x-1+x\sqrt{9-16x}\right)}{1-2x}} \, \mathrm dx = \frac{\pi^2}{8}.$$ Let $$I = \int\limits_0^{\sqrt 2 / 4}\frac{1}{\sqrt{x-x^2}}\arcsin\sqrt{\frac{(x-1)\left(x-1+x\sqrt{9-16x}\right)}{1-2x}} \, \mathrm dx. \tag{1}$$ The representation integral of ##\arcsin## is $$\arcsin u = \int\limits_{0}^{1} \frac{\mathrm dt}{\sqrt{1-t^2}}, \qquad 0 \leqslant u \leqslant 1.$$ Plugging identity above into ##(1)## with ##u...

Similar threads

Back
Top