pont) Find the following integral. Note that you can check your ar Se³√ VP dy=
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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![**Problem:** Find the following integral. Note that you can check your answer by ...
\[ \int \frac{5e^{3\sqrt{y}}}{\sqrt{y}} \, dy = \]
**Explanation:**
This problem involves the integration of a function with respect to \( y \). The integrand is given as a fraction where the numerator is \( 5e^{3\sqrt{y}} \) and the denominator is \( \sqrt{y} \).
- The expression \( e^{3\sqrt{y}} \) indicates an exponential function with the power raised to \( 3\sqrt{y} \).
- The denominator \(\sqrt{y}\) is the square root of \( y \).
To integrate this function, consider using a substitution method or integration by parts if applicable due to the presence of \( \sqrt{y} \) and the exponential function.](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2F58cffe43-d701-4c21-9740-08fe8d98ee79%2F34b1b085-0266-42ca-9648-6d8e9194c71e%2Fe8fp98g_processed.jpeg&w=3840&q=75)
Transcribed Image Text:**Problem:** Find the following integral. Note that you can check your answer by ...
\[ \int \frac{5e^{3\sqrt{y}}}{\sqrt{y}} \, dy = \]
**Explanation:**
This problem involves the integration of a function with respect to \( y \). The integrand is given as a fraction where the numerator is \( 5e^{3\sqrt{y}} \) and the denominator is \( \sqrt{y} \).
- The expression \( e^{3\sqrt{y}} \) indicates an exponential function with the power raised to \( 3\sqrt{y} \).
- The denominator \(\sqrt{y}\) is the square root of \( y \).
To integrate this function, consider using a substitution method or integration by parts if applicable due to the presence of \( \sqrt{y} \) and the exponential function.
![The image displays an integral problem, which is presented as follows:
\[
\int 3 \sin^5 x \cos x \, dx =
\]
The solution is expected to be written in the input box provided, followed by an integration constant, represented as \(+ C\). This setup appears to be part of an online educational platform where students can input their answers to mathematical problems.](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2F58cffe43-d701-4c21-9740-08fe8d98ee79%2F34b1b085-0266-42ca-9648-6d8e9194c71e%2Fk0mh7io_processed.jpeg&w=3840&q=75)
Transcribed Image Text:The image displays an integral problem, which is presented as follows:
\[
\int 3 \sin^5 x \cos x \, dx =
\]
The solution is expected to be written in the input box provided, followed by an integration constant, represented as \(+ C\). This setup appears to be part of an online educational platform where students can input their answers to mathematical problems.
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