1 / | | 5*x | e *sin(3*x) dx | / 0
Use integration by parts, noting that the integrand eventually repeats itself.
For the integrand :
Let and let .
Then .
For the integrand :
Let and let .
Then .
Notice that the integrand has repeated itself, so move it to one side:
Therefore,
Now simplify:
Add the constant of integration:
The answer is:
/ | 5*x 5*x | 5*x 3*cos(3*x)*e 5*e *sin(3*x) | e *sin(3*x) dx = C - --------------- + --------------- | 34 34 /
5 5 3 3*cos(3)*e 5*e *sin(3) -- - ----------- + ----------- 34 34 34
=
5 5 3 3*cos(3)*e 5*e *sin(3) -- - ----------- + ----------- 34 34 34
Use the examples entering the upper and lower limits of integration.