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12-51.

All of these integrals require the use of integration by parts.

Note: The following steps ignore the bounds of integration. Be sure to apply them at the end.
Let f = x2 and dg = exdx.
Then df = 2x dx and g = ex.

For the integral:
Let f = 2x and dg = exdx.
Then df = 2dx and g = ex.

You can now integrate the integral that is left without using integration by parts.

Use the same process outlined in part (a), but use e3x instead of ex.

Let f = x and dg = sin(x).

Let f = sin(x) and dg = sin(x)dx.

Now solve this equation for the original integral.