# How do you find the definite integral of #x^2dx / (x^3 + 9)# from #[-1, 1]#?

We want to find:

For this, we will use substitution. Let:

There are various ways this can be simplified:

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

To find the definite integral of ( \frac{x^2}{x^3 + 9} ) from ( -1 ) to ( 1 ), follow these steps:

- Evaluate the antiderivative of the given function ( \frac{x^2}{x^3 + 9} ).
- Substitute the upper limit (1) into the antiderivative and subtract the result from substituting the lower limit (-1).
- The difference will give you the value of the definite integral.

There is no elementary antiderivative for ( \frac{x^2}{x^3 + 9} ), so numerical methods or advanced techniques like contour integration may be needed to find the value of the definite integral.

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