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How do you integrate #int-12x^2(-4x^3+2)^-3# using substitution?

Answer 1

Isabella Ackerman

#-1/(2(-4x^3 +2)^(2)) +C#

#int -12x^2(-4x^3 +2)^-3 dx#

Let #u=-4x^3 +2#

#(du)/dx = -12x^2#

#(du) = -12x^2 dx#

now we substitute #int (u)^-3 du#

#-1/(2u^(2)) +C#

now we replace #u#

#-1/(2(-4x^3 +2)^(2)) +C#

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Answer 2

Ezekiel Alexander

To integrate ( \int -12x^2(-4x^3 + 2)^{-3} ) using substitution, you can let ( u = -4x^3 + 2 ). Then, find ( \frac{du}{dx} ) and solve for ( dx ). After that, substitute ( u ) and ( du ) into the integral. This will transform the integral into a simpler form, making it easier to solve.

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Answer from HIX Tutor

When evaluating a one-sided limit, you need to be careful when a quantity is approaching zero since its sign is different depending on which way it is approaching zero from. Let us look at some examples.