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Evaluate the integral by making the given substitution.$\int \frac{d t}{(1-6 t)^{4}}, \quad u=1-6 t$
$\frac{1}{18(1-6 t)^{3}}+C$
Calculus 1 / AB
Calculus 2 / BC
Chapter 5
Integrals
Section 4
The Substitution Rule
Integration Techniques
Missouri State University
Campbell University
Idaho State University
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So for this question, we have the integral of one over 60 to the power of four. Were amenity uses substitution off one over one minus 2 60 So the D use equal to negative six DT or D'You divided by negative six is equal to d T. So pulling the one out of majors won over negative six out. We can get that this is equal to you to the power of negative four, which is equal to you to the power off. Negative three divided by negative three. Most liked by negative one over six, which is equal to one over 18 times you to the power of native three. Back substituting. We end up with a final answer off one over 18 times one minus 62. The power off negative three.
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