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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.$$\int x(x-4)^{2 / 3} d x$$

Calculus 1 / AB

Chapter 28

Methods of Integration

Section 8

Integration by Trigonometric Substitution

Integrals

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calculate the integral, as…

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(a) Make an appropriate $u…

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(a) Make an appropriate u-…

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in the problem if you find the integral that is integration X into X -4. to the power of to upon three. The X solar does assume x minus four equals you. And dx become do you? Hence this country? Regional integration it is You plus four into U. to the power of to a .3 do you? This is equal to integration you did the power of £5.3 plus four U. to the power of 2.3 do you? And further this equals two three upon eight. Due to the power of eight upon three plus 12 upon +50 The power 5.3. Last see therefore this is equal to 15 years to the power of 8.3 Plus 96 U. to the power of 5.3 Over 40 Plus C. Now this is written as three upon 40 and two five U. to the power of eight upon 3 Plus 32 U. to the power of 5.3 blessing These equals three upon 40 Into five. u. 32 U. To the power of £5.3 plus six. Now further This is equal to three upon 40 Into five into X -4. Last 32 Into U. to the power of 5.3 plus c. So it is equal to three upon 40 and two five x -20 plus 32. You know the power of 5.3 Plus C equals two three upon 40 into five x plus 12 in two X -4 to the power of 5.3 plus the so we have this as the answer to the problem.

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