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This browser is pathetic for mathematical answers but here's the best that I can do:
Let u = 23x therefore du/dx = 23let dv/dx = e^(2x) therefore v = 1/2*e^(2x)
then, integrating by parts,
I = I(u*dv/dx) dx = u*v - I(du/dx*v) dx
= 23x*(1/2)*e^(2x) - I(23*(1/2)*e^(2x) dx
= 23/2*xe^(2x) - 23/2*I(e^(2x)) dx
= 23/2*xe^(2x) - 23/2*(1/2)*e^(2x)
= 23/2*xe^(2x) - 23/4*e^(2x)
or 23/4*e^(2x)*(2x - 1)
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