im trying to find the indefinate intergral of
dx/(3-7x)
the answer is supposed to have ln |v|, though i do not see how this fits in with the equation.
thank you in advance to those who can help me
dx/(3-7x)
the answer is supposed to have ln |v|, though i do not see how this fits in with the equation.
thank you in advance to those who can help me
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Let v = 3-7x.
Then, dv = -7dx.
So, dx = -(1/7)dv.
After making these substitutions, we have the integral of:
-(1/7v)dv.
Factor out the -(1/7) so that you have -(1/7) * integral of dv/v.
The integral of dv/v = ln|v|; we use || because ln only takes positive values.
So, you have -(1/7)*ln|v|.
This gives us -(1/7)*ln|3-7x|.
Then, dv = -7dx.
So, dx = -(1/7)dv.
After making these substitutions, we have the integral of:
-(1/7v)dv.
Factor out the -(1/7) so that you have -(1/7) * integral of dv/v.
The integral of dv/v = ln|v|; we use || because ln only takes positive values.
So, you have -(1/7)*ln|v|.
This gives us -(1/7)*ln|3-7x|.