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I need to find the minimum of this integral

F=∫ (αy^-1+βy^3+δxy)dx

where α, β and δ are constant; y is a function of x

the integral is calculated over the interval [0,L], where L is constant

I need to find the function y that minimizes the above-mentioned integral

The integral is subject to the following constraint

N=∫ydx

where N is a constant and the integral interval is again [0,L]

Anyone can help?

Is it possible to find an analytical solution?

Thanks

Ps:Sorry for the bad format, it's my first post

F=∫ (αy^-1+βy^3+δxy)dx

where α, β and δ are constant; y is a function of x

the integral is calculated over the interval [0,L], where L is constant

I need to find the function y that minimizes the above-mentioned integral

The integral is subject to the following constraint

N=∫ydx

where N is a constant and the integral interval is again [0,L]

Anyone can help?

Is it possible to find an analytical solution?

Thanks

Ps:Sorry for the bad format, it's my first post

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