My Math Forum Stuck on this integral

 Calculus Calculus Math Forum

May 19th, 2017, 12:06 PM   #1
Member

Joined: Jan 2017
From: California

Posts: 80
Thanks: 8

Stuck on this integral

Hi guys.

What is the best way to integrate this?

I can't seem to wrap my head around it.
Attached Images
 gif.gif (778 Bytes, 14 views)

Last edited by skipjack; May 20th, 2017 at 12:48 AM.

 May 19th, 2017, 12:34 PM #2 Math Team   Joined: Jul 2011 From: Texas Posts: 2,692 Thanks: 1351 if the integrand is $\left(x + \dfrac{5}{9}\right)^{3/2}$, then the antiderivative is $\dfrac{2}{5}\left(x + \dfrac{5}{9}\right)^{5/2} + C$ if the integrand is $\left(\dfrac{x + 5}{9}\right)^{3/2} = \dfrac{(x+5)^{3/2}}{27}$, then the antiderivative is $\dfrac{2}{135}\left(x + 5 \right)^{5/2} + C$ Thanks from v8archie and dthiaw
 May 19th, 2017, 12:53 PM #3 Math Team   Joined: Dec 2013 From: Colombia Posts: 7,118 Thanks: 2369 Math Focus: Mainly analysis and algebra It looks ideal for a simple $u$ substitution. Thanks from dthiaw
 May 20th, 2017, 03:41 AM #4 Global Moderator   Joined: Dec 2006 Posts: 18,443 Thanks: 1462 To try to find $\displaystyle \!\int\! f(x)dx$ using the substitution $x = g(u)$, where $g(u)$ is invertible and differentiable, find $\dfrac{dx}{du} = g^\prime\!(u)$, then use $\displaystyle \!\int\! f(x)dx = \!\int\! f(g(u))\frac{dx}{du}du = \!\int\! f(g(u))g^\prime\!(u)du$. After integrating, write the result in terms of $x$ (using the inverse of $g$ if necessary). Explicitly specifying the domain of $g$ is advisable to assist with that and simplifying $f(g(u))g^\prime\!(u)$. To find, for example, $\displaystyle \!\int\! \frac{1}{x^2\sqrt{1 - x^2}} dx$, where $0 < x < 1$, let $x = \cos(u)$, where $0 < u < \pi/2$, so that $\dfrac{dx}{du} = -\sin(u)$ and $\sqrt{1 - x^2} = \sin(u)$. This gives $\displaystyle \!\int\! \frac{1}{\cos^2(u)\sin(u)} (-\sin(u)) du = \!\int\! -\sec^2(u)du = -\tan(u) + \text{C} = -\frac{\sin(u)}{\cos(u)} + \text{C}$ (where $\text{C}$ is a constant), which equals $-\dfrac{\sqrt{1 - x^2}}{x} + \text{C}$. Thanks from dthiaw

 Tags integral, stuck

 Thread Tools Display Modes Linear Mode

 Similar Threads Thread Thread Starter Forum Replies Last Post KaiL Algebra 1 December 7th, 2016 04:07 AM natt010 Calculus 4 January 30th, 2016 09:41 AM CrimeAndPunishment Calculus 1 April 5th, 2014 04:52 PM Christine Calculus 3 March 1st, 2013 09:56 AM khalidd Algebra 1 September 9th, 2010 12:19 PM

 Contact - Home - Forums - Cryptocurrency Forum - Top