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