stuck on another problem.
Integrate:
1/(x * sqrt(x + 1))
Used u sub setting:
u = sqrt(x +1)
x = u^2 - 1
dx = 2udu
I end up with: -16/(u * (u^2 - 1))
Move out -16, and split u^2 -1 into (u + 1)(u - 1)
Used partial fractions; got A = -1, B = 0.5, C = 0.5.
I get: -lnabs(u) + 1/2lnabs(u -1) + 1/2lnabs(u + 1) + C
Substitute x back in, multiply by the -16 I moved out, and I get:
16lnabs(sqrt(x + 1) - 8lnabs(sqrt(x + 1) - 1) - 8lnabs(sqrt(x+1) +1) + C
And that seems to be wrong.
Found my error, forgot to factor out u.
Integrate:
1/(x * sqrt(x + 1))
Used u sub setting:
u = sqrt(x +1)
x = u^2 - 1
dx = 2udu
I end up with: -16/(u * (u^2 - 1))
Move out -16, and split u^2 -1 into (u + 1)(u - 1)
Used partial fractions; got A = -1, B = 0.5, C = 0.5.
I get: -lnabs(u) + 1/2lnabs(u -1) + 1/2lnabs(u + 1) + C
Substitute x back in, multiply by the -16 I moved out, and I get:
16lnabs(sqrt(x + 1) - 8lnabs(sqrt(x + 1) - 1) - 8lnabs(sqrt(x+1) +1) + C
And that seems to be wrong.
Found my error, forgot to factor out u.