1 / | | 2*x | e *cos(x) dx | / 0
Integral(E^(2*x)*cos(x), (x, 0, 1))
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:
/ | 2*x 2*x | 2*x e *sin(x) 2*cos(x)*e | e *cos(x) dx = C + ----------- + ------------- | 5 5 /
2 2 2 e *sin(1) 2*cos(1)*e - - + --------- + ----------- 5 5 5
=
2 2 2 e *sin(1) 2*cos(1)*e - - + --------- + ----------- 5 5 5
Use the examples entering the upper and lower limits of integration.