1 / | | / log(x)\ | |-------| | \log(10)/ | --------- dx | 3 | x | / 0
Integral((log(x)/log(10))/x^3, (x, 0, 1))
Let .
Then let and substitute :
The integral of a constant times a function is the constant times the integral of the function:
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:
So, the result is:
Now substitute back in:
Now simplify:
Add the constant of integration:
The answer is:
/ | 1 log(x) | / log(x)\ - ---- - ------ | |-------| 2 2 | \log(10)/ 4*x 2*x | --------- dx = C + --------------- | 3 log(10) | x | /
Use the examples entering the upper and lower limits of integration.