oo / | | 4 | --------------- dx | / 2 \ | x*\log (x) + 1/ | / 1
Integral(4/((x*(log(x)^2 + 1))), (x, 1, oo))
The integral of a constant times a function is the constant times the integral of the function:
Don't know the steps in finding this integral.
But the integral is
So, the result is:
Now simplify:
Add the constant of integration:
The answer is:
/ | | 4 / 2 \ | --------------- dx = C + 4*RootSum\4*z + 1, i -> i*log(2*i + log(x))/ | / 2 \ | x*\log (x) + 1/ | /
oo / | | 1 4* | --------------- dx | / 2 \ | x*\1 + log (x)/ | / 1
=
oo / | | 1 4* | --------------- dx | / 2 \ | x*\1 + log (x)/ | / 1
4*Integral(1/(x*(1 + log(x)^2)), (x, 1, oo))
Use the examples entering the upper and lower limits of integration.