### Home > CALC > Chapter Ch12 > Lesson 12.1.2 > Problem 12-21

12-21.

Use substitution. Let *u* = ln(3*x*).

Use integration by parts. Let *f* = sin(2*x*) and *dg* = *e ^{x}dx*.

Then

*df*= 2cos(2

*x*)

*dx*and

*g*=

*e*.

^{x}Use integration by parts on the integral in Step 2.

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

Then

*df*= –2sin(2

*x*)

*dx*and

*g*=

*e*.

^{x}Use partial fraction decomposition.

Rewrite the denominator of the integrand using Steps 1 and 2.

You should recognize the integrand as a form of the derivative of a special function.

Use algebra to get the original integral expression by itself.