What is (4x^4+2)^{-3}*16x^3dx ?

The solution to (4x^4+2)^{-3}*16x^3dx is (2x^3dx)/((2x^4+1)^3)

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simplify (4x^4+2)^{-3}*16x^3dx

simplify

(4 x^{4} + 2)^{- 3} \cdot 16 x^{3} d x

\frac{2 x ^{3} d x}{( 2 x ^{4} + 1 ) ^{3}}

Solution steps

(4 x^{4} + 2)^{- 3} \cdot 16 x^{3} d x

Apply exponent rule:

a^{- b} = \frac{1}{a ^{b}}

= 16 \cdot \frac{1}{( 4 x ^{4} + 2 ) ^{3}} x^{3} d x

Multiply fractions:

a \cdot \frac{b}{c} = \frac{a \cdot b}{c}

= \frac{1 \cdot 16 x ^{3} d x}{( 4 x ^{4} + 2 ) ^{3}}

Multiply the numbers:

1 \cdot 16 = 16

= \frac{16 x ^{3} d x}{( 4 x ^{4} + 2 ) ^{3}}

Factor

(4 x^{4} + 2)^{3} : 8 (2 x^{4} + 1)^{3}

= \frac{16 x ^{3} d x}{8 ( 2 x ^{4} + 1 ) ^{3}}

Divide the numbers:

\frac{16}{8} = 2

= \frac{2 x ^{3} d x}{( 2 x ^{4} + 1 ) ^{3}}

10 e^{- 10 x}

(5 mn) (6 m^{2} n^{5})

co m v er t i r^{17} ce n t ima l es

x^{2} e^{x} d x

e^{- 6 \cdot (7)}

What is (4x^4+2)^{-3}*16x^3dx ?
The solution to (4x^4+2)^{-3}*16x^3dx is (2x^3dx)/((2x^4+1)^3)