Evaluate the Indefinite Integral. + C Lax 1x - 3 (1x² - 6x + 5)4 -dx
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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Question
![### Evaluate the Indefinite Integral
Evaluate the integral:
\[
\int \frac{1x - 3}{(1x^2 - 6x + 5)^4} \, dx
\]
\[
\boxed{\phantom{C}} + C
\]
### Explanation
In this problem, you are tasked with evaluating an indefinite integral involving a rational function. The integral has the form of a fraction where the numerator is linear and the denominator is a power of a quadratic polynomial. The result of evaluating this integral will include an arbitrary constant \( C \), which indicates the general solution to an indefinite integration problem.](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2F58cffe43-d701-4c21-9740-08fe8d98ee79%2Fbc908d5b-0712-45d0-bd4e-9410ec0afd77%2Fblwjlsw_processed.jpeg&w=3840&q=75)
Transcribed Image Text:### Evaluate the Indefinite Integral
Evaluate the integral:
\[
\int \frac{1x - 3}{(1x^2 - 6x + 5)^4} \, dx
\]
\[
\boxed{\phantom{C}} + C
\]
### Explanation
In this problem, you are tasked with evaluating an indefinite integral involving a rational function. The integral has the form of a fraction where the numerator is linear and the denominator is a power of a quadratic polynomial. The result of evaluating this integral will include an arbitrary constant \( C \), which indicates the general solution to an indefinite integration problem.
![**Problem:** Find the following integral. Note that you can check your answer by [method not visible].
\[ \int \frac{5e^{3\sqrt{y}}}{\sqrt{y}} \, dy = \]
**Explanation:** The task is to evaluate the integral of the function \( \frac{5e^{3\sqrt{y}}}{\sqrt{y}} \) with respect to \( y \). This requires techniques of integration which could involve substitution to simplify the expression.](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2F58cffe43-d701-4c21-9740-08fe8d98ee79%2Fbc908d5b-0712-45d0-bd4e-9410ec0afd77%2Fav7w27j_processed.jpeg&w=3840&q=75)
Transcribed Image Text:**Problem:** Find the following integral. Note that you can check your answer by [method not visible].
\[ \int \frac{5e^{3\sqrt{y}}}{\sqrt{y}} \, dy = \]
**Explanation:** The task is to evaluate the integral of the function \( \frac{5e^{3\sqrt{y}}}{\sqrt{y}} \) with respect to \( y \). This requires techniques of integration which could involve substitution to simplify the expression.
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