1 / | | ___ 2 | \/ x *log (x)*x dx | / 0
Integral(sqrt(x)*log(x)^2*x, (x, 0, 1))
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.
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:
Now simplify:
Add the constant of integration:
The answer is:
/ | 5/2 5/2 5/2 2 | ___ 2 16*x 8*x *log(x) 2*x *log (x) | \/ x *log (x)*x dx = C + ------- - ------------- + -------------- | 125 25 5 /
Use the examples entering the upper and lower limits of integration.