# How do you integrate #xln(x^2)#?

Step 1. Produce the integration by parts formula or find it somewhere online...

Step 2. Use the integration by parts formula and implicit differentiation to produce your final result...

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

To integrate ( x \ln(x^2) ), we can use integration by parts. Let ( u = \ln(x^2) ) and ( dv = x , dx ). Then differentiate ( u ) to find ( du ), and integrate ( dv ) to find ( v ). After that, apply the integration by parts formula:

[ \int u , dv = uv - \int v , du ]

Here are the steps:

- Let ( u = \ln(x^2) ), so ( du = \frac{1}{x^2} , dx ).
- Let ( dv = x , dx ), so ( v = \frac{x^2}{2} ).

Now apply the integration by parts formula:

[ \int x \ln(x^2) , dx = \frac{x^2 \ln(x^2)}{2} - \int \frac{x^2}{2} \cdot \frac{1}{x^2} , dx ]

Simplify the integral on the right-hand side:

[ \frac{x^2 \ln(x^2)}{2} - \int \frac{1}{2} , dx ]

Integrate the remaining term:

[ \frac{x^2 \ln(x^2)}{2} - \frac{x}{2} + C ]

So the integral of ( x \ln(x^2) ) is ( \frac{x^2 \ln(x^2)}{2} - \frac{x}{2} + 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.

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