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