1 / | | 2 | t - 1 | ------ dt | t | / 0
Integral((t^2 - 1)/t, (t, 0, 1))
There are multiple ways to do this integral.
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 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:
The integral of is .
So, the result is:
The result is:
So, the result is:
Now substitute back in:
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 .
So, the result is:
The result is:
Add the constant of integration:
The answer is:
/ | | 2 2 / 2\ | t - 1 t log\t / | ------ dt = C + -- - ------- | t 2 2 | /
Use the examples entering the upper and lower limits of integration.