Home > Calculus > Integrals of Rational Functions

How do you evaluate the integral #int lnx/xdx#?

Answer 1

Paisley Johnson

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

We have that:

#d/(dx) (lnx) = 1/x#

so:

#int lnx/x dx = int lnx d(lnx) = 1/2(lnx)^2+C#

By signing up, you agree to our Terms of Service and Privacy Policy

Answer 2

Emma Aldridge

To evaluate the integral ∫(ln(x))/x dx, you can use integration by parts. Let u = ln(x) and dv = dx/x. Then differentiate u to get du and integrate dv to get v. Afterward, apply the integration by parts formula: ∫u dv = uv - ∫v du. Finally, substitute the values of u, v, du, and dv into the formula and solve for the integral. The result is ∫(ln(x))/x dx = (ln(x))^2/2 + C, where C is the constant of integration.

By signing up, you agree to our Terms of Service and Privacy Policy

Answer from HIX Tutor

When evaluating a one-sided limit, you need to be careful when a quantity is approaching zero since its sign is different depending on which way it is approaching zero from. Let us look at some examples.