### Home > CALC > Chapter 12 > Lesson 12.1.4 > Problem 12-51

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* = *x*^{2} and *dg* = *e ^{x}dx*.

Then

*df*= 2

*x dx*and

*g*=

*e*.

^{x}For the integral:

Let *f* = 2*x* and *dg* = *e ^{x}dx*.

Then

*df*= 2

*dx*and

*g*=

*e*.

^{x}You can now integrate the integral that is left without using integration by parts.

Use the same process outlined in part (a), but use *e*^{3}* ^{x}* instead of

*e*.

^{x}Let *f* = *x* and *dg* = sin(*x*).

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

Now solve this equation for the original integral.