oo / | | 2 | / 4\ | \1 + x / | --------- dx | 3 | x | / 2
Integral((1 + x^4)^2/x^3, (x, 2, oo))
There are multiple ways to do this integral.
Rewrite the integrand:
Integrate term-by-term:
The integral of is when :
The integral of a constant times a function is the constant times the integral of the function:
The integral of is when :
So, the result is:
The integral of is when :
The result is:
Rewrite the integrand:
Let .
Then let and substitute :
The integral of a constant times a function is the constant times the integral of the function:
Rewrite the integrand:
Integrate term-by-term:
The integral of is when :
The integral of a constant is the constant times the variable of integration:
The integral of is when :
The result is:
So, the result is:
Now substitute back in:
Now simplify:
Add the constant of integration:
The answer is:
/ | | 2 | / 4\ 6 | \1 + x / 2 1 x | --------- dx = C + x - ---- + -- | 3 2 6 | x 2*x | /
Use the examples entering the upper and lower limits of integration.