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# meer integration watch

1. im feeling really really stuupid.....

integrate v dv
g-kv

(g and k are constants)
2. v/(g - kv) = -1/k + (g/k) / (g - kv)
3. Oh that is good. I dont know how ive got through p5......

How do you work that out like.. just standard thing
4. Write the numerator v as a multiple of the denominator (g - kv) plus a constant:

v = SOMETHING * (g - kv) + SOMETHING ELSE,
v = (-1/k) * (g - kv) + g/k.

That gives

v/(g - kv) = -1/k + (g/k) / (g - kv),

which integrates to

constant - v/k - (g/k^2) ln|g-kv|.

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Updated: June 30, 2004
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