1 / | | (x*log(x) - x + c1*x + c2) dx | / 0
Integral(x*log(x) - x + c1*x + c2, (x, 0, 1))
Integrate term-by-term:
The integral of a constant is the constant times the variable of integration:
Integrate term-by-term:
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:
Integrate term-by-term:
There are multiple ways to do this integral.
Let .
Then let and substitute :
Use integration by parts:
Let and let .
Then .
To find :
Let .
Then let and substitute :
The integral of a constant times a function is the constant times the integral of the function:
The integral of the exponential function is itself.
So, the result is:
Now substitute back in:
Now evaluate the sub-integral.
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 a constant times a function is the constant times the integral of the function:
The integral of the exponential function is itself.
So, the result is:
Now substitute back in:
So, the result is:
Now substitute back in:
Use integration by parts:
Let and let .
Then .
To find :
The integral of is when :
Now evaluate the sub-integral.
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 times a function is the constant times the integral of the function:
The integral of is when :
So, the result is:
The result is:
The result is:
The result is:
Now simplify:
Add the constant of integration:
The answer is:
/ 2 2 2 | 3*x c1*x x *log(x) | (x*log(x) - x + c1*x + c2) dx = C - ---- + c2*x + ----- + --------- | 4 2 2 /
3 c1 - - + c2 + -- 4 2
=
3 c1 - - + c2 + -- 4 2
-3/4 + c2 + c1/2
Use the examples entering the upper and lower limits of integration.