Evaluate the integral \( \int x e^x \, dx \) using integration by parts.

Evaluate the integral \( \int x^2 e^x \, dx \) using integration by parts twice.

Evaluate the integral \( \int x \sin(x^2) \, dx \) using integration by parts and substitution.

Evaluate the indefinite integral.

$\int {\ln }^{3}xdx$

Compute the integral:

${\int }_0^1{x}^{11}{e}^{x^3}dx$