x 3e (-2) ¿Cuál es la integral indefinida de xdx? Gracias

t=-2x

x=-t/2

x^3=-t^3/8

dx=(-1/2)dt

Integral original = integral-T3/8 * e t *(1/2)dt.

=(1/16)integral t^3e^tdt

Segmentación

=(1/16)entero t^3d(e^t)

=(1/16)[e t * t 3-integración 3t 2d(e t)]

=(1/16)[e t * 3-3t2e t+6 entero TD ( e t)]

=(1/16)[e t * t 3-3t2e t+6te t-6 entero 1d (e t)]

=(1/16) [e ^t*t^3-3t^2e^t+6te^t-6e^t]

T=-2x

=(1/16)[-8x ^3e ^(-2x)-12x^2e^(-2x)-12xe^(-2x)-6e^(-2x)]

=(-1/8)[4x^3+ 6x^ 2+6x+3]e^(-2x)