Problem 42 Easy Difficulty

Certain algebraic integrals can be transformed into integrable form with the appropriate algebraic substitution. For an expression of the form $(a x+b)^{p / q},$ a substitution of the form $u=(a x+b)^{1 / q}$ may put it into an integrable form. Use this type of substitution for the given integrals.
$$\int \frac{x^{2} d x}{(4 x+1)^{5 / 2}}$$

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Basic Technical Mathematics with Calculus

Chapter 28

Methods of Integration

Section 8

Integration by Trigonometric Substitution

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Video Transcript

in the problem we have the integration that is X squared dx over four X plus one. To the power of 5.2. So here are four X plus one is assumed as aid four DX Becomes Desert. Or we have jade minus one upon four. To the power to that equals X squared No, this is Regina has integration. Jade- went to the power of two. All right, 16 intriguing to the power of 5.2. Dessert upon four. This is equal to 1.64. Integration Get a squad plus 1 -2 Jade Over due to the power 5.2 dessert. No, this is written as one upon 64 Integration J to the power to -5.2 Plus. due to the power -5.2 -2. Integrated Part 1 -5.2. Indigent. This is equal to When upon 64 integration Due to the poor -1.2 Plus Singer. to the power -5.2 -2 J. to the power -3 upon to digit. So this is equal to 1.64 christian two. Rather it is under break it To get to the power one upon to upon one Plus to get to the power -3 upon to over -3 Plus four G. to the power of -1 upon to over one plus. See now this is equal to When I found 64 and two. To get to the part one upon to -2 upon three. Get to the power minus three upon two plus four. Get the power -1 upon two plus the sea. I thought that written as Went up on 32, get to the power half -1. About 96 J to the power -3 upon to Plus one upon 16. Get the power minus one upon two plus C Further putting the values of jade, therefore we have. These equals to one upon 32 four X plus one to the power of half minus one upon 96 four X plus went to the power of -3 upon to Plus one upon 16 four X. Plus we went to the power of minus one upon two plus C. This is the answer.

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Basic Technical Mathematics with Calculus

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Problem 42 Easy Difficulty

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Watch More Solved Questions in Chapter 28

Video Transcript

Allyn J. Washington, Richard S. Evans

Basic Technical Mathematics with Calculus

Catherine R.

Kayleah T.

Samuel H.

Michael J.

Precalculus Review - Intro

Functions on the Real Line - Overview

Basic Technical Mathematics with Calculus

Catherine R.

Kayleah T.

Samuel H.

Michael J.

Precalculus Review - Intro

Functions on the Real Line - Overview

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

Catherine R.

Kayleah T.

Samuel H.

Michael J.

Precalculus Review - Intro

Functions on the Real Line - Overview

Allyn J. Washington, Richard S. Evans

Basic Technical Mathematics with Calculus