Question

Bioengineering major here, with a confusing integral that I can't crack. From a class on biotransport phenomena. See below!

Answer 1

\[Te ^{\frac{ 2br ^{2} - ar ^{4} }{ 4 }} = C _{1} \int\limits_{ }^{ } e ^{\frac{ 2br ^{2} - ar ^{4} }{ 4 }} dr\]

Answer 2

T is a function of r, btw. Not easy to play around with, so I can't derive both sides and try to find the derivative of the left.

Answer 3

Not too clear exactly what you're looking for.
Is T(r) defined as:
\(\Large T(r)e ^{\frac{ 2br ^{2} - ar ^{4} }{ 4 }} = C _{1} \int\limits_{ }^{ } e ^{\frac{ 2br ^{2} - ar ^{4} }{ 4 }} dr\)
therefore
\(\Large T(r) =\frac{ C _{1} \int\limits_{ }^{ } e ^{\frac{ 2br ^{2} - ar ^{4} }{ 4 }} dr}{e ^{\frac{ 2br ^{2} - ar ^{4} }{ 4 }}}\)
or something else?