Problem

Integrate each of the given functions. $$\int \fr…

Problem 18 Easy Difficulty

Integrate each of the given functions.
$$\int_{0}^{0.5} \frac{3 e^{3 x}}{e^{x-1}} d x$$

Answer

$\frac{3}{2}\left(e^{2}-e\right)$

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Calculus 1 / AB

Basic Technical Mathematics with Calculus

Chapter 28

Methods of Integration

Section 3

The Exponential Form

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Video Transcript

mhm. Yes. We went to evaluate the following into rule the integral from 2.53 Either three X over E to the x minus one dx. Or as I've written to make simpler on the right. The integral from 0 to 0.53 Each of the two X plus one dx. This question is testing our knowledge of methods of integration. We've already learned the power rule and the log arrhythmic form in this particular problem. We're being tasked to use the exponential integration formula which states that the integral of either the U T U S E U plus. See the concept of integration. We won't need to see for this question cause it's a definite integral. However, we can still use this formula. So if we identify you and do you we can solve us whatever in the power of E. Or the exponent E. So it must be the U S. Two X plus one. The U S to D X. Thus we have a factor of 3/2 extra and are integral that we carry over to the solution. So are integral is three house integral to the u d u or three halfs either to express one from 2.5. This has solution three half c squared minus E.

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Allyn J. Washington, Richard S. Evans

Basic Technical Mathematics with Calculus

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Problem

Integrate each of the given functions. $$\int \fr…

Problem 18 Easy Difficulty

Integrate each of the given functions.
$$\int_{0}^{0.5} \frac{3 e^{3 x}}{e^{x-1}} d x$$

Answer

$\frac{3}{2}\left(e^{2}-e\right)$

Related Courses

Basic Technical Mathematics with Calculus

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Watch More Solved Questions in Chapter 28

Video Transcript

Allyn J. Washington, Richard S. Evans

Basic Technical Mathematics with Calculus

Grace H.

Catherine R.

Anna Marie V.

Joseph L.

Precalculus Review - Intro

Functions on the Real Line - Overview

$\frac{3}{2}\left(e^{2}-e\right)$

Basic Technical Mathematics with Calculus

Grace H.

Catherine R.

Anna Marie V.

Joseph L.

Precalculus Review - Intro

Functions on the Real Line - Overview

Allyn J. Washington, Richard S. EvansBasic Technical Mathematics with Calculus

Grace H.

Catherine R.

Anna Marie V.

Joseph L.

Precalculus Review - Intro

Functions on the Real Line - Overview

Allyn J. Washington, Richard S. Evans

Basic Technical Mathematics with Calculus