#6, 38, 46, p. 492 -- Integration by Parts homework

Integrate[(x-1)Sin[Pi*x],x]

38

Integrate[t^3*Exp[-t^2],t]

46

f[x_]:=(x^2)Sin[2*x]
g[x_]=Integrate[(x^2)Sin[2*x],x]

Plot[{f[x],g[x]},{x,0,2Pi}]