1 / | | 3 | x *log(x)*1 dx | / 0
Integral(x^3*log(x)*1, (x, 0, 1))
There are multiple ways to do this integral.
Let .
Then let and substitute :
Use integration by parts:
Let and let .
Then .
To find :
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:
The integral of the exponential function is itself.
So, the result is:
Now substitute back in:
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 a constant is the constant times the variable of integration:
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:
Now simplify:
Add the constant of integration:
The answer is:
/ | 4 4 | 3 x x *log(x) | x *log(x)*1 dx = C - -- + --------- | 16 4 /
Use the examples entering the upper and lower limits of integration.