Calculus Calculus Math Forum

 September 17th, 2016, 03:34 AM #11 Senior Member   Joined: Aug 2016 From: morocco Posts: 273 Thanks: 32 it' of de form $\int u^\alpha.u' f September 17th, 2016, 03:36 AM #12 Senior Member Joined: Aug 2016 From: morocco Posts: 273 Thanks: 32 with x=1/t it becomes of the form$\int u^a u' f$ September 17th, 2016, 08:12 AM #13 Senior Member Joined: Aug 2016 From: morocco Posts: 273 Thanks: 32 don't take into account posts 11 and 12. with the substitution$x=\frac{1}{t}$, your integral becomes of the form$\int u^a u'$Last edited by abdallahhammam; September 17th, 2016 at 08:15 AM. September 17th, 2016, 09:30 PM #14 Global Moderator Joined: Oct 2008 From: London, Ontario, Canada - The Forest City Posts: 7,981 Thanks: 1166 Math Focus: Elementary mathematics and beyond$\displaystyle \int(x^2+1)^{-3/2}\,dx=\int\frac{1}{(x^2+1)\sqrt{x^2+1}}\,dx= \int\frac{x} {x(x^2+1)\sqrt{x^2+1}}\,dx$$$u=\frac{x}{\sqrt{x^2+1}},\quad du=(x^2+1)^{-3/2}\,dx$$ ... etc ...    September 17th, 2016, 11:01 PM #15 Math Team Joined: Dec 2013 From: Colombia Posts: 7,700 Thanks: 2682 Math Focus: Mainly analysis and algebra I like the$\frac1tidea although it essentially becomes the single substitution that I used. The one I came up with was \begin{aligned} \int \left(1+x^2\right)^{-\frac32} \,\mathrm dx &= \int {1 \over \left(\sqrt{1+x^2}\right)^3} \,\mathrm dx \\ &= \int {1 \over \left(\sqrt{x^2\left(\frac1{x^2}+1\right)}\right)^ 3} \,\mathrm dx \\ &= \int {1 \over \left(x\sqrt{\frac1{x^2}+1}\right)^3} \,\mathrm dx \\ &= \int {1 \over x^3\left(\sqrt{\frac1{x^2}+1}\right)^3} \,\mathrm dx \\ &= \int x^{-3}\left(\tfrac1{x^2}+1\right)^{-\frac32} \,\mathrm dx \\ \end{aligned} And thenu = 1 + x^{-2}\$. Thanks from greg1313 Tags required, substitution Thread Tools Show Printable Version Email this Page Display Modes Linear Mode Switch to Hybrid Mode Switch to Threaded Mode Similar Threads Thread Thread Starter Forum Replies Last Post prabhatpustake Calculus 0 June 15th, 2014 05:11 AM qamath09 Algebra 6 June 11th, 2013 11:18 PM saravananr Algebra 10 September 7th, 2012 05:03 AM ymharshe Linear Algebra 1 May 10th, 2009 05:26 PM Useless1 Calculus 2 May 19th, 2008 12:46 PM

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