Problem

Evaluate the definite integral. $ \displaystyl…

01:01

Problem 56 Hard Difficulty

Evaluate the definite integral.

$ \displaystyle \int^3_0 \frac{dx}{5x + 1} $

Answer

$\frac{4 \ln 2}{5}$

More Answers

01:18

Frank L.

Topics

Integrals

Integration

Book Cover for Calculus: Early Tra…

Calculus: Early Transcendentals

Chapter 5

Integrals

Section 5

The Substitution Rule

Discussion

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Missouri State University

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Video Transcript

from the problem we've been given, the first thing you can do is pull out the constant 1/5. Then we can rewrite the integral. Now we know as we established that you is five. Expose one rate. It's the denominator. Therefore, do you is simply five d backs. Therefore now the limits of integration change from five times 05 times three plus one on the top, which is 16 and five time zero post went on the bottom, which is simply one. So the constant remains on the outside as we just established our limits or from our bouncer from 1 to 16. Take the integral and we end up with four natural log with two divided by five.

Amrita B.

Topics

Integrals

Integration

Book Cover for Calculus: Early Tra…

Calculus: Early Transcendentals

Chapter 5

Integrals

Section 5

The Substitution Rule

Top Calculus 1 / AB Educators

Catherine R.

Missouri State University

Anna Marie V.

Campbell University

Samuel H.

University of Nottingham

Michael J.

Idaho State University