5 / | | x*sin(3*x) dx | / 0
Integral(x*sin(3*x), (x, 0, 5))
Use integration by parts:
Let and let .
Then .
To find :
Let .
Then let and substitute :
The integral of a constant times a function is the constant times the integral of the function:
The integral of sine is negative cosine:
So, the result is:
Now substitute back in:
Now evaluate the sub-integral.
The integral of a constant times a function is the constant times the integral of the function:
Let .
Then let and substitute :
The integral of a constant times a function is the constant times the integral of the function:
The integral of cosine is sine:
So, the result is:
Now substitute back in:
So, the result is:
Add the constant of integration:
The answer is:
/ | sin(3*x) x*cos(3*x) | x*sin(3*x) dx = C + -------- - ---------- | 9 3 /
5*cos(15) sin(15) - --------- + ------- 3 9
=
5*cos(15) sin(15) - --------- + ------- 3 9
-5*cos(15)/3 + sin(15)/9
Use the examples entering the upper and lower limits of integration.