- #1
whatisphysics
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iamalexalright said:Try using u = x^8
iamalexalright said:Alright, the integral is:
[tex]\int x^{7}e^{x^{8}}dx[/tex]
I'll choose u = x^8
[tex]du = 8x^{7}dx[/tex]
Here is where you had an issue before, notice that in the original integral I do have x^7dx in it ! This implies I don't need to divide by x^7, I just use the substitution:
[tex]\frac{1}{8}du = x^{7}dx[/tex]
Can you finish it from here?
An indefinite integral is a mathematical operation that finds the most general antiderivative of a given function. It is represented by the symbol ∫, and is the reverse operation of differentiation.
Evaluating indefinite integrals can be complex and require a thorough understanding of calculus principles. Sometimes, the integrand may not have a closed-form solution, making it difficult to find the antiderivative. Additionally, a mistake in the integration process can also lead to being stuck.
There are several techniques that can be used to evaluate indefinite integrals, such as substitution, integration by parts, and partial fractions. It is important to identify which technique would be most appropriate for the given integrand, and to carefully follow the steps to find the antiderivative.
Yes, many scientific calculators have a built-in function to evaluate indefinite integrals. However, it is still important to have a basic understanding of the concepts and techniques involved in solving these integrals.
You can check your answer by taking the derivative of the antiderivative you found. If the resulting function is the original integrand, then your answer is correct. Additionally, you can also use online integration tools or ask for help from a math tutor or teacher.