Question

can some one help me get where find where the 1/5 came from

Answer 1

\[\int u^4du=\frac{u^5}{5}\]

Answer 2

Take the derivative of (1/5)u^5 and you'll see that it's u^4! I usually end up taking the derivative of my integrals to check that I'm right since it can feel like falling in a black hole some times.

Answer 3

More generally,\[\int x^n\ dx =\frac{x^{n+1}}{n+1}+C\]

Answer 4

Taking the constant out,\[{-1 \over 30}\int u^4du\]Which is\[-{1 \over 30}\left({u^5 \over 5} +\rm C\right) = -{1 \over 30} \]

Answer 5

Sorry for the incomplete answer...\[{-1 \over 30}\cdot {1 \over5}\left(u^5 \right)+\rm C\]