# How do you integrate #(x^3)(e^(x^2))dx#?

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

To integrate the expression (\int x^3 e^{x^2} , dx), you can use the substitution method. Let (u = x^2), then (du = 2x , dx). Substitute (u) and (du) into the integral to get (\frac{1}{2} \int u e^u , du). Now, integrate by parts with (dv = e^u , du) and (u = u). This yields (\frac{1}{2}(u e^u - \int e^u , du)). Integrating (e^u) with respect to (u) gives (\frac{1}{2}(u e^u - e^u) + C), where (C) is the constant of integration. Finally, substitute (u = x^2) back into the expression to get (\frac{1}{2}(x^2 e^{x^2} - e^{x^2}) + C).

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