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