Question

What is the integral from 0 to 1 of `x*sqrt(x^2+8)`?

Answer 1

Try this:
`intxsqrt(x^2+8)dx=`
But `d[x^2+8]=2xdx`
So:
`1/2intsqrt(x^2+8)d[x^2+8]=`
`=1/2int(x^2+8)^(1/2)d[x^2+8]=1/2((x^2+8)^(3/2))/(3/2)`
Between `0` and `1`:
`=1/3(x^2+8)^(3/2)|_0^1`=`9-8/3sqrt(8)=9-16/3sqrt(2)`