1. ## Integrating fractions

Having a dum blonde moment...

Would...

$\displaystyle \int{\frac{2u+7}{u^6}}du$

be...

$\displaystyle \int{2u+7}du\int{\frac{1}{u^6}}du$

or...

$\displaystyle \int{(2u+7)(u^{-6})}$
with the product rule...

2. Always be on the lookout for an opportunity to split the numerator...

$\displaystyle \int{\frac{2u}{u^6}}+{\frac{7}{u^6}}\ du$

3. Originally Posted by darksupernova
Having a dum blonde moment...

Would...

$\displaystyle \int{\frac{2u+7}{u^6}}du$

be...

$\displaystyle \int{2u+7}du\int{\frac{1}{u^6}}du$

or...

$\displaystyle \int{(2u+7)(u^{-6})}$
with the product rule...

$\displaystyle \int{\frac{2u+7}{u^6}}du$ $\displaystyle = \int{\frac{2u}{u^{6}}}$ $\displaystyle +\frac{7}{u^{6}}du$ $\displaystyle = \frac{2}{u^{5}}+ \frac{7}{u^{6}}du$

Then just bring U's up to the top line

i.e. $\displaystyle \int{2u^{-5}}+{7u^{-6}}du$ and integrate normally w.r.t u

4. thank you both