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Alona [7]
3 years ago
11

∫x(x-6)³dx by using substitution u=x-6​

Mathematics
1 answer:
Agata [3.3K]3 years ago
7 0

Answer:

\large\boxed{\int\bigg(x(x-6)^3\bigg)dx=\dfrac{1}{5}(x-6)^5+\dfrac{3}{2}(x-6)^4+C}

Step-by-step explanation:

\int\bigg(x(x-6)^3\bigg)dx\Rightarrow\left[\begin{array}{ccc}x-6=u\\x=u+6\\dx=du\end{array}\right]\Rightarrow\int\bigg((u+6)u^3\bigg)du\\\\=\int(u^4+6u^3)du=\dfrac{1}{5}u^5+\dfrac{6}{4}u^4+C=\dfrac{1}{5}(x-6)^5+\dfrac{3}{2}(x-6)^4+C

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Mice21 [21]
When you multiply 5 by 1 you get 5. When you multiply 5 by 2 you get 10. If you keep doing this, you get a list of multiples of 5.

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All of these numbers end in either 5 or 0. We can do the same with 2's and 10's.

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2 years ago
Evaluate the numerical expression. 9.6 – 10.8 ÷ 0.6
Lorico [155]
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The answer is -8.4

Hope this helps and have a great day!
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3 years ago
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Mark wants to eat one last cookie from the cookie jar in the jar they are fire truck which of cookies six peanut butter cookies
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3 years ago
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