# Integrating e^(8x^2) - Solutions & Steps

• abhaiitg
In summary, to solve an integral with e^(8x^2), use the substitution method by letting u = 8x^2 and then integrating e^u using the power rule. You can also use integration by parts, but it may be more complicated. There is a general formula for integrating e^(ax^2), and special cases include when the exponent is negative.
abhaiitg

## Homework Statement

integerate e^(8x^2)

## The Attempt at a Solution

its seems it is not having closed integeral form.

They're asking you to take an indefinite integral of that? It doesn't have an elementary antiderivative, but the erf(x) is used to take definite integrals, so if they haven't taught you about that, I'm guessing you have the problem wrong.

no erff function can be integerated i guess

some wolfram but i don't know how i could use dat formulae here!

## 1. How do I solve an integral with e^(8x^2)?

To solve an integral with e^(8x^2), you can use the substitution method. Let u = 8x^2 and then use the power rule to find the integral of e^u. After integrating, substitute back in 8x^2 for u to get the final solution.

## 2. What are the steps for integrating e^(8x^2)?

The steps for integrating e^(8x^2) are:

1. Use substitution to replace e^(8x^2) with u
2. Find the integral of e^u using the power rule
3. Substitute back in 8x^2 for u to get the final solution

## 3. Can I use integration by parts to solve e^(8x^2)?

Yes, you can use integration by parts to solve e^(8x^2), but it may be more complicated and time-consuming compared to using the substitution method.

## 4. Is there a general formula for integrating e^(ax^2)?

Yes, there is a general formula for integrating e^(ax^2). It is:

∫e^(ax^2)dx = √(π/a) * e^(ax^2) * erf(√a * x) + C

where erf is the error function.

## 5. Are there any special cases when integrating e^(8x^2)?

Yes, if the exponent is a negative number, the integral becomes a simple inverse function. For example, ∫ e^(-8x^2) dx = √(π/8) * erfc(√8 * x) + C, where erfc is the complementary error function.

• Calculus and Beyond Homework Help
Replies
10
Views
629
• Calculus and Beyond Homework Help
Replies
2
Views
594
• Calculus and Beyond Homework Help
Replies
7
Views
835
• Calculus and Beyond Homework Help
Replies
11
Views
1K
• Calculus and Beyond Homework Help
Replies
9
Views
2K
• Calculus and Beyond Homework Help
Replies
11
Views
1K
• Calculus and Beyond Homework Help
Replies
24
Views
2K
• Calculus and Beyond Homework Help
Replies
6
Views
1K
• Calculus and Beyond Homework Help
Replies
16
Views
1K
• Calculus and Beyond Homework Help
Replies
11
Views
3K