Explanation Given Information: The function is ∫ e 2 x cos ( e 2 x + 1 ) d x . Formula Used: The following integration formula is used: ∫ cos x d x = sin x + C The derivation formula, d d x a = 0 , where a is all-natural numbers. And, d d x e n x = n e n x , where n is all-natural numbers. Calculation: Consider the provided function ∫ e 2 x cos ( e 2 x + 1 ) d x . Replace the parenthetical expression with variable u . u = e 2 x + 1 Determine the derivative of u with respect to x. d u d x = d d x ( e 2 x + 1 ) = d d x ( e 2 x ) + d d x 1 = 2 e 2 x + 0 = 2 e 2 x Determine the value of d x . d x = 1 2 e 2 x d u Substitute the value of d x into the integral

Student Solutions Manual for Waner/Costenoble's Finite Math and Applied Calculus, 7th

7th Edition

ISBN: 9781337275972

Author: Waner, Stefan; Costenoble, Steven

Publisher: Cengage Learning

See similar textbooks

Concept explainers

Riemann Sum

Riemann Sums is a special type of approximation of the area under a curve by dividing it into multiple simple shapes like rectangles or trapezoids and is used in integrals when finite sums are involved. Figuring out the area of a curve is complex hence t…

Riemann Integral

Bernhard Riemann's integral was the first systematic description of the integral of a function on an interval in the branch of mathematics known as real analysis.

Videos

Question

Chapter 16.3, Problem 19E

To determine

To calculate: The solution of the integral function ∫e2xcos(e2x+1)dx.

Expert Solution & Answer

Want to see the full answer?

Check out a sample textbook solution

See solution

Chapter 16.3, Problem 18E

Chapter 16.3, Problem 20E

Students have asked these similar questions

Two cars start moving from the same point. One travels south at 60 mi/h and the other travels west at 25 mi/h. At what rate (in mi/h) is the distance between the cars increasing four hours later? Step 1 Using the diagram of a right triangle given below, the relation between x, y, and z is z² = x²+ +12 x Step 2 We must find dz/dt. Differentiating both sides and simplifying gives us the following. 2z dz dt dx 2x. +2y dt dx dy dz x +y dt dt dt 2z dy dt × dx (x+y dt dy dt

An elastic rope is attached to the ground at the positions shown in the picture. The rope is being pulled up along the dotted line. Assume the units are meters. 9 ground level Assume that x is increasing at a rate of 3 meters/sec. (a) Write as a function of x: 0= (b) When x=10, the angle is changing at a rate of rad/sec. (c) Let L be the the left hand piece of rope and R the right hand piece of rope. When x=10, is the rate of change of L larger than the rate of change of R? ○ Yes ○ No

4.1 Basic Rules of Differentiation. 1. Find the derivative of each function. Write answers with positive exponents. Label your derivatives with appropriate derivative notation. a) y=8x-5x3 4 X b) y=-50 √x+11x -5 c) p(x)=-10x²+6x3³

Chapter 16 Solutions

Student Solutions Manual for Waner/Costenoble's Finite Math and Applied Calculus, 7th

Ch. 16.1 - Prob. 1E Ch. 16.1 - Prob. 2E Ch. 16.1 - Prob. 3E Ch. 16.1 - Prob. 4E Ch. 16.1 - Prob. 5E Ch. 16.1 - Prob. 6E Ch. 16.1 - Prob. 7E Ch. 16.1 - Prob. 8E Ch. 16.1 - Prob. 9E Ch. 16.1 - Prob. 10E

Knowledge Booster

$Calculus$

Learn more about

Need a deep-dive on the concept behind this application? Look no further. Learn more about this topic, calculus and related others by exploring similar questions and additional content below.

The solution of the integral function ∫ e 2 x cos ( e 2 x + 1 ) d x .

Solution Summary: The author explains how to calculate the integral function displaystyle

Concept explainers

Videos

To calculate: The solution of the integral function ∫e2xcos(e2x+1)dx.

Want to see the full answer?

Chapter 16 Solutions