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[SOLVED] integration by parts question
This is part of a larger problem but I'm just not sure if I have the right answer.
edit: this is integral of ln(x-7)dx i just can't seem to figure out how to make it in latex
u-substituion:
[tex]u = x - 7[/tex]
[tex]du = dx[/tex]
Integration by parts to get
[tex]\intlnudu = ulnu - \int1du[/tex]
[tex] = ulnu - u[/tex]
[tex] = (x - 7)ln(x - 7) - (y - 7) + C[/tex]
Now my only problem with this answer is that it gives 7 + C as part of the answer, and I can't recall ever seeing a constant + C as the answer for any integral.
I actually plugged the equation into this integral finder:
http://integrals.wolfram.com/index.jsp
And it told me that it was
[tex](x-7)ln(x-7) - x[/tex]
I'm guessing the +C is a given.
I would just leave it at +C and go on but its part of a differential equation so the value of C ends up being important...
Homework Statement
This is part of a larger problem but I'm just not sure if I have the right answer.
edit: this is integral of ln(x-7)dx i just can't seem to figure out how to make it in latex
Homework Equations
The Attempt at a Solution
u-substituion:
[tex]u = x - 7[/tex]
[tex]du = dx[/tex]
Integration by parts to get
[tex]\intlnudu = ulnu - \int1du[/tex]
[tex] = ulnu - u[/tex]
[tex] = (x - 7)ln(x - 7) - (y - 7) + C[/tex]
Now my only problem with this answer is that it gives 7 + C as part of the answer, and I can't recall ever seeing a constant + C as the answer for any integral.
I actually plugged the equation into this integral finder:
http://integrals.wolfram.com/index.jsp
And it told me that it was
[tex](x-7)ln(x-7) - x[/tex]
I'm guessing the +C is a given.
I would just leave it at +C and go on but its part of a differential equation so the value of C ends up being important...
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