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Evaluate 3x e cos (5x) dx.

Evaluate 3x e cos (5x) dx.

Calculus: Early Transcendentals
Calculus: Early Transcendentals
8th Edition
ISBN:9781285741550
Author:James Stewart
Publisher:James Stewart
Chapter1: Functions And Models
Section: Chapter Questions
Problem 1RCC: (a) What is a function? What are its domain and range? (b) What is the graph of a function? (c) How...
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This is being solved using the [u dv = u v - v du] method

I am stuck in this loop of the integral of e^3xcos5x I found the answer on Mathway to be:

(1/3cos(5x)e^3x+5/9sin(5x)e^3x)9/34+C 

But I do not understand how to get past the picture with the green ink.

Thanks in advance!

**Problem Statement:** Evaluate the integral \(\int e^{3x} \cos(5x) \, dx\). **Explanation:** This is a problem of integration involving the exponential function \(e^{3x}\) and the trigonometric function \(\cos(5x)\). To solve this, you may employ integration techniques such as integration by parts or using specific formulas for integrals of products of exponential and trigonometric functions. If using integration by parts, recall the formula: \[ \int u \, dv = uv - \int v \, du \] You would select \(u\) and \(dv\) from the components of the function \(e^{3x} \cos(5x)\). For this problem, you might also consider Euler's formula or specific integration formulas used for exponential and trigonometric forms, recognizing this as a standard problem type in calculus. Consider exploring these methods to determine the integral.
Transcribed Image Text:**Problem Statement:** Evaluate the integral \(\int e^{3x} \cos(5x) \, dx\). **Explanation:** This is a problem of integration involving the exponential function \(e^{3x}\) and the trigonometric function \(\cos(5x)\). To solve this, you may employ integration techniques such as integration by parts or using specific formulas for integrals of products of exponential and trigonometric functions. If using integration by parts, recall the formula: \[ \int u \, dv = uv - \int v \, du \] You would select \(u\) and \(dv\) from the components of the function \(e^{3x} \cos(5x)\). For this problem, you might also consider Euler's formula or specific integration formulas used for exponential and trigonometric forms, recognizing this as a standard problem type in calculus. Consider exploring these methods to determine the integral.
The image contains mathematical expressions written in green ink on lined paper. The expressions involve exponential functions, trigonometric functions, and integrals. The transcription of the text is as follows: 1/3 e^(3x) Cos 5x + 5/9 e^(3x) Sin 5x - (25/9) ∫ e^(3x) Cos 5x This expression includes: - Exponential functions of the form e^(3x). - Trigonometric functions Cos 5x and Sin 5x. - An integral of the product e^(3x) Cos 5x. These components are likely part of a mathematical problem involving differential equations or integration techniques.
Transcribed Image Text:The image contains mathematical expressions written in green ink on lined paper. The expressions involve exponential functions, trigonometric functions, and integrals. The transcription of the text is as follows: 1/3 e^(3x) Cos 5x + 5/9 e^(3x) Sin 5x - (25/9) ∫ e^(3x) Cos 5x This expression includes: - Exponential functions of the form e^(3x). - Trigonometric functions Cos 5x and Sin 5x. - An integral of the product e^(3x) Cos 5x. These components are likely part of a mathematical problem involving differential equations or integration techniques.
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