Question

Evaluate the integral:

\[\int\limits_{}^{}ye ^{0.2y}dy\]
The problem we are having is the antiderivative of
\[e ^{0.2y}.\] We decided to split the problem into:
u = y
\[uv = e^{0.2y}\]
We just aren't sure where to go from here. Help?

Answer 1

`\int\limits_{}^{}ye ^(0.2y)dy \\ \\u=y,du=dy \\dv=e ^{(y)/(5)}dy,v=\int\limits_{}^{}e ^{ (y)/(5) }dy=5e ^{ (y)/(5) } \\ \\ \int\limits_{}^{}ye ^{(y)/(5) }}dy=uv- \int\limits {v} \, du=y 5e ^{ (y)/(5) }-\int\limits {5e ^{ (y)/(5) }} \, dy= 5ye ^{ (y)/(5) }-25e ^{ (y)/(5) }=5e ^{ (y)/(5) }(y-5)`