4 years ago

Is having a multiplication sign outside the parentheses the same as not?

Mathematics

2 answers:

katrin2010 [14]4 years ago

8 0

I believe it's the same

Lera25 [3.4K]4 years ago

4 0

Is having a multiplication sing outside the parentheses the same.

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

rewona [7]

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

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