Differentiate y = 5xe2x+1 with respect to x and hence, find ∫x(e^{2x+1}) dx.

Solution: 1/2(x)(e^{2x+1}) – 1/4(e^{2x+1}) + C

dy/dx = 5x(e^{2x+1})(2) + 5(e^{2x+1})

=10x(e^{2x+1}) + 5(e^{2x+1})

5x(e^{2x+1}) = ∫10x(e^{2x+1}) + 5(e^{2x+1}) dx

5x(e^{2x+1}) = 10∫x(e^{2x+1}) dx + 5∫(e^{2x+1}) dx

10∫x(e^{2x+1}) dx + 5/2(e^{2x+1}) = 5x(e^{2x+1})

10∫x(e^{2x+1}) dx = 5x(e^{2x+1}) -5/2(e^{2x+1})

∫x(e^{2x+1}) dx = 1/2(x)(e^{2x+1}) – 1/4(e^{2x+1}) + C