Evaluate the integral. (Use C for the constant of integration.) 4e3x + e3x dx √4e3 Step 1 We are given the following. 14 [4e³x + 4e3x + e3x dx We note that we can simplify the integrand as follows. 4e³ 4e3x + e3x dx = = √4(1 e³r 3. e lee3x dx Step 2 We have rewritten the integral as follows. [4 4e3x ee3 3x dx We will now try to find some function u = g(x) in the integrand whose differential du = g'(x) dx also occurs, apart from a constant factor. Here we notice that if we let u = e³x, then du = 14e³x ee³x dx = [( 3 43 3e3x eu du 303x 1). dx. Applying this substitution gives us the following. Step 3 We can now apply the integration formula a 4 eu du = 3 4( eu du = e. Doing so gives the following result where C is the constant of integration. C Seu du )+c Finally, we write our answer in terms of x, recalling that we let u = e3x. Doing so gives the following result. (Use C for the constant of integration.)

Evaluate the integral. (Use C for the constant of integration.) 4e3x + e3x dx √4e3 Step 1 We are given the following. 14 [4e³x + 4e3x + e3x dx We note that we can simplify the integrand as follows. 4e³ 4e3x + e3x dx = = √4(1 e³r 3. e lee3x dx Step 2 We have rewritten the integral as follows. [4 4e3x ee3 3x dx We will now try to find some function u = g(x) in the integrand whose differential du = g'(x) dx also occurs, apart from a constant factor. Here we notice that if we let u = e³x, then du = 14e³x ee³x dx = [( 3 43 3e3x eu du 303x 1). dx. Applying this substitution gives us the following. Step 3 We can now apply the integration formula a 4 eu du = 3 4( eu du = e. Doing so gives the following result where C is the constant of integration. C Seu du )+c Finally, we write our answer in terms of x, recalling that we let u = e3x. Doing so gives the following result. (Use C for the constant of integration.)

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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