specific integral problem.help me please!?
specific integral between -1 and 0.5 of (X^2)/(X-1)
it seems so simple,i dont understand why i cant solve this!
thx!!
Update:i mean-i have to solve this by calling (x^2) t or any other letter..and then its derivative is 2x but i suupose to make it (x-1)
for ex-if the real derivative is 2x and i have to make it x i make it 2x and also divide with 1/2.
so how can i make x+1 into 2x ??
Comments
First we can divide a little bit:
...x²:(x-1) = x+1+(1/(x-1))
-(x²-x)
--------
.......x
.....-(x-1)
------------
...........1
.........-1
------------
...........0
Now
0.5................0.5
..∫x²:(x-1)dx = ∫x+1+(1/(x-1))]dx
-1..................-1
................................0.5
= [(1/2)x²+x+ln|x-1|]
................................-1
= (1/8)+(1/2)+ln(1/2)-[(1/2)-1+ln2]
= (9/8)-ln2-ln2
= (9/8)-2*ln2
= (9/8)-ln4,
=========
because ln(1/2) = ln(1)-ln(2) = -ln2
and 2*ln2 = ln(2²) = ln4
@graingert: Everyone is able to solve
integrals with wolframalpha!
supp.: I don´t really understand your second question!
Please rewrite it!
supp2.: You are in integration by substituting. This does
not work in our exemple! Here we have to divide by
divission of polynomials.
integral X^2/(X-1) dX = X^2/2+X+log(X-1)-3/2+constant...
integral_(-1)^0.5X^2/(-1+X) dX = -0.261294...