1 answer

How do you evaluate the integral #int 1/(x(1+(lnx)^2)#?

Question:

How do you evaluate the integral #int 1/(x(1+(lnx)^2)#?

Answers

#int1/(x(1+(lnx)^2))dx=arctan(lnx)+C#

Explanation:

Let #u=lnx#. This implies that #du=1/xdx#.

#int1/(x(1+(lnx)^2))dx=int1/(1+(lnx)^2)(1/xdx)=int1/(1+u^2)du#

This is the arctangent integral:

#=arctan(u)+C=arctan(lnx)+C#

.

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