Question

Evaluate the indefinite integral. (Use symbolic notation and fractions where needed. Use C for the arbitrary constant. Absorb into C as much as possible.) ? x(7x + 9)¹? dx = 1/49 ( 1/12 t² - 9/11 t¹¹ ) + C

          Evaluate the indefinite integral.
(Use symbolic notation and fractions where needed. Use C for the arbitrary constant. Absorb into C as much as possible.)
? x(7x + 9)¹? dx = 1/49 ( 1/12 t² - 9/11 t¹¹ ) + C
        
Evaluate the indefinite integral.
(Use symbolic notation and fractions where needed. Use C for the arbitrary constant. Absorb into C as much as possible.)
? x(7x + 9)¹? dx = 1/49 ( 1/12 t² - 9/11 t¹¹ ) + C

Added by Robert S.

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Calculus: Early Transcendentals
Calculus: Early Transcendentals
James Stewart 8th Edition
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Evaluate the indefinite integral. (Use symbolic notation and fractions where needed. Use C for the arbitrary constant. Absorb into C as much as possible.)
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Transcript

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00:01 Right so in this problem we want to evaluate the indefinite integral of x times 7x plus 9th to the power of 10th dx we do not want to expand 7x plus 9 to the 10th that will be way too much work is that we want to make a use of decision let you be equal to 7x plus 9 the differential du is just going to equal to 7 times the x x so 1 over 7th du is going to equal to dx note that if u is equal to 7x plus 9th that would imply that we can solve for x in terms of u first 7x is going to equal to u minus 9th and x is going to be u minus 9 divided by 7th let's keep that in mind so this is like our side work the integral is now going to be equal to the integral with respect to you that is the integral of x which is u minus 9th divided by 7th this is x times 7x plus 9th which is u to the power…
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