+0  
 
0
255
1
avatar+62 

Need some help with this one :-) Thanks guys!

mathmeme  May 17, 2017
 #1
avatar
+1

Take the integral:
 integral(2000 x^2014 + 14)/(x^2015 - x) dx
For the integral (2000 x^2014 + 14)/(x^2015 - x), write (2000 x^2014 + 14)/(x^2015 - x) as (2000 x^1999 + 14/x^15)/(x^2000 - 1/x^14):
 = integral(2000 x^1999 + 14/x^15)/(x^2000 - 1/x^14) dx
For the integrand (2000 x^1999 + 14/x^15)/(x^2000 - 1/x^14), substitute u = x^2000 - 1/x^14 and du = (2000 x^1999 + 14/x^15) dx:
 = integral1/u du
The integral of 1/u is log(u):
 = log(u) + constant
Substitute back for u = x^2000 - 1/x^14:
 = log((x^2014 - 1)/x^14) + constant
Which is equivalent for restricted x values to:
Answer: | = log(1 - x^2014) - 14 log(x) + constant

Guest May 17, 2017

27 Online Users

avatar
avatar
avatar
avatar
avatar

New Privacy Policy

We use cookies to personalise content and advertisements and to analyse access to our website. Furthermore, our partners for online advertising receive information about your use of our website.
For more information: our cookie policy and privacy policy.