Evaluate the Integral ?

int_1^2((v^3-3v^6)/v^4)dv
I got to the point where I used the properties of integrals and my answer was ln2 +5. Where F(b)-F(a). The answer was ln2+7. Any ideas where I went wrong. I don't see where they are getting 7 from.

1 Answer
Aug 11, 2018

ln2-7.

Explanation:

int_1^2((v^3-3v^6)/v^4)dv,

=int_1^2(v^3/v^4-3v^6/v^4)dv,

=int_1^2(1/v-3v^2)dv,

=[ln|v|-3*v^(2+1)/(2+1)]_1^2,

=[ln|v|-v^3]_1^2,

=[{ln|2|-2^3}-{ln|1|-1^3}],

=ln2-8-0+1.

rArr int_1^2((v^3-3v^6)/v^4)dv=ln2-7.