How do you integrate? I try again and again.
#int x^10sqrt(x-2)dx#
1 Answer
Jun 19, 2018
Use the substitution
Explanation:
Let
#I=intx^10sqrt(x-2)dx#
Apply the substitution
#I=2int(u^2+2)^10u^2du#
Apply binomial expansion:
#I=2int{sum_(n=0)^10((10),(n))u^(2n)2^(10-n)}u^2du#
Rearrange:
#I=sum_(n=0)^10((10),(n))2^(11-n)intu^(2n+2)du#
Integrate directly:
#I=sum_(n=0)^10((10),(n))2^(11-n)/(2n+3)u^(2n+3)+C#
Reverse the substitution:
#I=sum_(n=0)^10((10),(n))2^(11-n)/(2n+3)(x-2)^((2n+3)/2)+C#