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

This is the arctangent integral:

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

To evaluate the integral (\int \frac{1}{x(1+(\ln x)^2)}), we can use the substitution method. Let (u = \ln x), then (du = \frac{1}{x} dx). Substituting these into the integral gives:

[ \int \frac{1}{x(1+(\ln x)^2)} , dx = \int \frac{1}{1+u^2} , du ]

Now, this integral is in a form that we can easily integrate using the arctangent function:

[ \int \frac{1}{1+u^2} , du = \arctan(u) + C ]

Finally, substituting back (u = \ln x) and simplifying gives the result:

[ \int \frac{1}{x(1+(\ln x)^2)} , dx = \arctan(\ln x) + C ]

where (C) is the constant of integration.

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

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.

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.

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.

- How do you integrate #int xarcsecx# by parts from #[2,4]#?
- Integration of (1/((x+(x^2+1)^(1/2))^3 at limit 0 to infinite ?
- How do you integrate #int x^3 e^x dx # using integration by parts?
- What is #f(x) = int (x-1)^3 dx# if #f(-1) = 1 #?
- How do you integrate #int(x+1)/((x-3)(x-1)(x+4))# using partial fractions?

- 98% accuracy study help
- Covers math, physics, chemistry, biology, and more
- Step-by-step, in-depth guides
- Readily available 24/7