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

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Answer 1 · 2016-08-16T00:58:56

#-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#