Integration by Tabular Method

Topic : Integration by Tabular Method
Question : Find ∫x³ Cos 2x dx


Hints :
∫x^n Cos ax dx
Take u = x^n
dv = Cos ax dx

For patterns like
∫x^n Sin ax dx , ∫x^n Cos ax dx ,
∫x^n e^(ax) dx we use tabular method


Solution :

∫x³ Cos 2x dx
u = x³ and dv = Cos 2x











+x³(Sin 2x)/2 - 3x²(-Cos 2x)/4 + 6x(-Sin 2x)/8 - 6(Cos 2x)/16
=(x³Sin 2x)/2 + 3/4 *(x²Cos 2x) - 6/8 *(xSin 2x) - 6/16 *(Cos 2x) + c