f(x) = | tan-1(x9) dx f(x) = C + > n = 0
Advanced Engineering Mathematics
10th Edition
ISBN:9780470458365
Author:Erwin Kreyszig
Publisher:Erwin Kreyszig
Chapter2: Second-order Linear Odes
Section: Chapter Questions
Problem 1RQ
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Evaluate the indefinite
![The given mathematical expression for the function \( f(x) \) is represented as an integral and a series:
1. **Integral Representation:**
\[
f(x) = \int \tan^{-1}(x^9) \, dx
\]
This is the integral of the inverse tangent function, \(\tan^{-1}\), applied to \(x^9\) with respect to \(x\).
2. **Series Representation:**
\[
f(x) = C + \sum_{n=0}^{\infty}
\]
The function is also expressed as a series, summed from \(n = 0\) to infinity. The constant \(C\) represents the constant of integration. The empty box indicates that the series terms are missing or need to be specified.
This equation is typically explored in the context of calculus, particularly when discussing techniques for integrating inverse trigonometric functions and representing functions as infinite series.](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2F0c47e9c0-f79d-42e2-ab04-7acfa45cd478%2Fb0261c5b-6b66-4512-9154-57c6a991a8aa%2F00nxhcc_processed.jpeg&w=3840&q=75)
Transcribed Image Text:The given mathematical expression for the function \( f(x) \) is represented as an integral and a series:
1. **Integral Representation:**
\[
f(x) = \int \tan^{-1}(x^9) \, dx
\]
This is the integral of the inverse tangent function, \(\tan^{-1}\), applied to \(x^9\) with respect to \(x\).
2. **Series Representation:**
\[
f(x) = C + \sum_{n=0}^{\infty}
\]
The function is also expressed as a series, summed from \(n = 0\) to infinity. The constant \(C\) represents the constant of integration. The empty box indicates that the series terms are missing or need to be specified.
This equation is typically explored in the context of calculus, particularly when discussing techniques for integrating inverse trigonometric functions and representing functions as infinite series.
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