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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?

Verified Answer :

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

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