# How do you integrate #int ln x^2 dx # using integration by parts?

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

To integrate ( \int \ln(x^2) , dx ) using integration by parts, let's designate ( u = \ln(x^2) ) and ( dv = dx ).

Differentiating ( u ), we get ( du = \frac{1}{x^2} \cdot 2x , dx = \frac{2}{x} , dx ).

Integrating ( dv ), we get ( v = x ).

Now, using the integration by parts formula ( \int u , dv = uv - \int v , du ), we have:

[ \int \ln(x^2) , dx = x \ln(x^2) - \int x \cdot \frac{2}{x} , dx ]

[ = x \ln(x^2) - 2 \int dx ]

[ = x \ln(x^2) - 2x + 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 (e^x)/sqrt(e^(2x) +16)dx# using trigonometric substitution?
- How do you integrate #inte^(3x)cos^2xdx# using integration by parts?
- What is #f(x) = int (x+1)/((x+5)(x-4) ) dx# if #f(2)=1 #?
- How do you integrate #(x^2-x-8)/((x+1)(x^2+5x+6))# using partial fractions?
- How do you use partial fractions to find the integral #int (x+1)/(x^2+4x+3) dx#?

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