Integration..help please!!

integrate (x^3)(3^x) dx by using integration by parts

∫x^3*(3^x) dx

u = x^3

dv = (3^x) dx

v = (3^x)/ln(3)

du = 3x^2 dx

uv - ∫v du

x^3*(3^x)/ln(3) - 3/ln(3)*∫x^2*(3^x) dx

Integrate by parts again:

u = x^2

dv = 3^(x) dx

v = 3^(x)/ln(3)

du = 2x dx

x^3*(3^x)/ln(3) - 3/ln(3)*[x^2*(3^x)/ln(3) - 2/ln(3)*∫x*3^(x) dx]

Integrate by parts again:

u = x

dv = 3^(x) dx

v = 3^(x)/ln(3)

du = dx

x^3*(3^x)/ln(3) - 3/ln(3)*[x^2*(3^x)/ln(3) - 2/ln(3)*(x*3^(x)/ln(3) - 3^(x)/ln²(3))] + C

x^3*(3^x)/ln(3) - 3*x^2*(3^(x))/ln²(3) + 6x*3^(x)/ln^3(3) - 6*3^(x)/ln^4(3) + C

∫ (x^3)(3^x)dx

let u = x^3......dv = 3^(x)
............................3^(x)
du = 3x^2dx v = -----------
............................ln(3)

∫ udv = uv - ∫ vdu

....x^3[3^(x)]..........3
= ----------------- - --------- ∫ x^2[3^(x)]dx
........ln(3).............ln(3)


integrating by parts again..

let u = x^2....dv = 3^(x)
..........................3^(x)
.du = 2xdx v = -------------
...........................ln(3)


....x^3[3^(x)]..........3........x^2 [3^(x)].........2....
= ----------------- - ----------- [ ---------------- -.-------- .∫ x [3^(x)]dx ]
........ln (3).............ln (3).........ln (3).......ln (3)

....x^3[3^(x)]..........3x^2[3^(x)]....…
=------------------ - ----------------------- + ----------- ∫ x [3^(x)]dx
.....ln (3)..................ln^2 (3)...........ln^2 (3)


we use integration by parts again..

let u = x.....dv = 3^(x)
......................3^(x)
du = dx..v = ----------
......................ln(3)


....x^3[3^(x)]..........3x^2[3^(x)]....… [3^ (x)]..... 1
=------------------ - ----------------------- + ----------- [---------------- - ------- ∫ 3 ^(x) dx]