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