How do you integrate #int x /sqrt( 81 - x^4 )dx# using trigonometric substitution?
1 Answer
Sep 19, 2016
Explanation:
We should apply the substitution
#intx/sqrt(81-x^4)dx=1/2int(2xdx)/sqrt(81-(x^2)^2)=1/2int(9costhetad theta)/sqrt(81-81sin^2theta)#
Note that
#=1/2int(costhetad theta)/sqrt(1-sin^2theta)#
Recall that
#=1/2intd theta=1/2theta+C#
From
#=1/2arcsin(x^2/9)+C#