1 / | | 2 | x - 81 | ------- dx | x + 9 | / 0
Integral((x^2 - 81)/(x + 9), (x, 0, 1))
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 is the constant times the variable of integration:
The result is:
Rewrite the integrand:
Integrate term-by-term:
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 a constant times a function is the constant times the integral of the function:
Let .
Then let and substitute :
The integral of is .
Now substitute back in:
So, the result is:
The result is:
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 is .
Now substitute back in:
So, the result is:
The result is:
Now simplify:
Add the constant of integration:
The answer is:
/ | | 2 2 | x - 81 x | ------- dx = C + -- - 9*x | x + 9 2 | /
Use the examples entering the upper and lower limits of integration.