pi / | | 2 | x *sin(5*x) dx | / -pi
Integral(x^2*sin(5*x), (x, -pi, pi))
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.
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 cosine is sine:
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 sine is negative cosine:
So, the result is:
Now substitute back in:
So, the result is:
Add the constant of integration:
The answer is:
/ | 2 | 2 2*cos(5*x) x *cos(5*x) 2*x*sin(5*x) | x *sin(5*x) dx = C + ---------- - ----------- + ------------ | 125 5 25 /
Use the examples entering the upper and lower limits of integration.