1 / | | 2 | 6*x *cos(3*x) dx | / 0
Integral(6*x^2*cos(3*x), (x, 0, 1))
The integral of a constant times a function is the constant times the integral of the function:
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.
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:
So, the result is:
Add the constant of integration:
The answer is:
/ | | 2 4*sin(3*x) 2 4*x*cos(3*x) | 6*x *cos(3*x) dx = C - ---------- + 2*x *sin(3*x) + ------------ | 9 3 /
4*cos(3) 14*sin(3) -------- + --------- 3 9
=
4*cos(3) 14*sin(3) -------- + --------- 3 9
Use the examples entering the upper and lower limits of integration.