What is the integral of e^{2ln(y)}*e^y ?

The integral of e^{2ln(y)}*e^y is y^2e^y-2(e^yy-e^y)+C

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integral of e^{2ln(y)}*e^y

\int e^{2 l n (y)} \cdot e^{y} d y

y^{2} e^{y} - 2 (e^{y} y - e^{y}) + C

Solution steps

\int e^{2 l n (y)} e^{y} d y

Simplify

e^{2 l n (y)} : y^{2}

= \int e^{y} y^{2} d y

Apply Integration By Parts

= y^{2} e^{y} - \int 2 y e^{y} d y

\int 2 y e^{y} d y = 2 (e^{y} y - e^{y})

= y^{2} e^{y} - 2 (e^{y} y - e^{y})

Add a constant to the solution

= y^{2} e^{y} - 2 (e^{y} y - e^{y}) + C

What is the integral of e^{2ln(y)}*e^y ?
The integral of e^{2ln(y)}*e^y is y^2e^y-2(e^yy-e^y)+C