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IceJOKER [234]
2 years ago
7

How do I solve this using the substitution method for finding anti derivatives?

Mathematics
1 answer:
rewona [7]2 years ago
6 0
A bit blurry, but if I'm making it out correctly, that's

\displaystyle\int t\sqrt{(t^2-9)^3}\,\mathrm dt=\int t(t^2-9)^{3/2}\,\mathrm dt

Set u=t^2-9. Then \mathrm du=2t\,\mathrm dt, or t\,\mathrm dt=\dfrac{\mathrm du}2. The integral is then equivalent to

\displaystyle u^{3/2}\dfrac{\mathrm du}2=\frac12\int u^{3/2}\,\mathrm du
=\dfrac12\dfrac{u^{5/2}}{\frac52}+C
=\dfrac12\times\dfrac25u^{5/2}+C
=\dfrac15u^{5/2}+C
=\dfrac15(t^2-9)^{5/2}+C
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B.

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8 0
3 years ago
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marshall27 [118]

Answer:

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Step-by-step explanation:

Given as :

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I.e x = \frac{8}{12} +  \frac{7.5}{9}

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3 0
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4 0
2 years ago
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garri49 [273]
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Does work


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Answer:

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Step-by-step explanation:

3 0
2 years ago
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