∫[0→5] x³/(x²+1)dx
=∫[0→5] (x³+x-x)/(x²+1)dx
=∫[0→5] xdx-∫[0→5] x/(x²+1)dx
=(1/2)x²-(1/2)∫[0→5] 1/(x²+1)d(x²)
=(1/2)x²-(1/2)ln(x²+1) |[0→5]
=25/2-(1/2)ln26
∫[0→5] x³/(x²+1)dx
=∫[0→5] (x³+x-x)/(x²+1)dx
=∫[0→5] xdx-∫[0→5] x/(x²+1)dx
=(1/2)x²-(1/2)∫[0→5] 1/(x²+1)d(x²)
=(1/2)x²-(1/2)ln(x²+1) |[0→5]
=25/2-(1/2)ln26