1 / | | 2 | x + 1 | ------ dx | x + 2 | / 0
Integral((x^2 + 1)/(x + 2), (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 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:
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:
Let .
Then let and substitute :
The integral of is .
Now substitute back in:
The result is:
Add the constant of integration:
The answer is:
/ | | 2 2 | x + 1 x | ------ dx = C + -- - 2*x + 5*log(2 + x) | x + 2 2 | /
-3/2 - 5*log(2) + 5*log(3)
=
-3/2 - 5*log(2) + 5*log(3)
-3/2 - 5*log(2) + 5*log(3)
Use the examples entering the upper and lower limits of integration.