oo / | | 2 / 3 \ | x *cos\3*x + 5/ dx | / 1
Integral(x^2*cos(3*x^3 + 5), (x, 1, oo))
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 simplify:
Add the constant of integration:
The answer is:
/ | / 3 \ | 2 / 3 \ sin\3*x + 5/ | x *cos\3*x + 5/ dx = C + ------------- | 9 /
1 sin(8) 1 sin(8) <- - - ------, - - ------> 9 9 9 9
=
1 sin(8) 1 sin(8) <- - - ------, - - ------> 9 9 9 9
Use the examples entering the upper and lower limits of integration.