How do you integrate $\int - 12 x^{2} {(- 4 x^{3} + 2)}^{- 3}$ $int-12x^2(-4x^3+2)^-3$ using substitution?

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Answer 1 · 2016-08-16T00:58:56

$- \frac{1}{2 {(- 4 x^{3} + 2)}^{2}} + C$ $-1/(2(-4x^3 +2)^(2)) +C$

$\int - 12 x^{2} {(- 4 x^{3} + 2)}^{- 3} d x$ $int -12x^2(-4x^3 +2)^-3 dx$

Let $u = - 4 x^{3} + 2$ $u=-4x^3 +2$

$\frac{d u}{d x} = - 12 x^{2}$ $(du)/dx = -12x^2$

$(d u) = - 12 x^{2} d x$ $(du) = -12x^2 dx$

now we substitute
$\int {(u)}^{- 3} d u$ $int (u)^-3 du$

$- \frac{1}{2 u^{2}} + C$ $-1/(2u^(2)) +C$

now we replace $u$ $u$

$- \frac{1}{2 {(- 4 x^{3} + 2)}^{2}} + C$ $-1/(2(-4x^3 +2)^(2)) +C$

How do you integrate ∫−12x2(−4x3+2)−3int-12x^2(-4x^3+2)^-3 using substitution?