What is 8/(sqrt((x^3+x^2+1)^3)) ?

The solution to 8/(sqrt((x^3+x^2+1)^3)) is 8/(sqrt(x^3+x^2+1)(x^3+x^2+1))

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simplify 8/(sqrt((x^3+x^2+1)^3))

simplify

\frac{8}{( x ^{3} + x ^{2} + 1 ) ^{3}}

\frac{8}{x ^{3} + x ^{2} + 1 ( x ^{3} + x ^{2} + 1 )}

Solution steps

\frac{8}{( x ^{3} + x ^{2} + 1 ) ^{3}}

Apply exponent rule:

a^{b + c} = a^{b} \cdot a^{c}

(x^{3} + x^{2} + 1)^{2 + 1} = (x^{3} + x^{2} + 1)^{2} (x^{3} + x^{2} + 1)

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

Apply radical rule:

ab = a b,

assuming

a \geq 0, b \geq 0

(x^{3} + x^{2} + 1)^{2} (x^{3} + x^{2} + 1) = (x^{3} + x^{2} + 1)^{2} x^{3} + x^{2} + 1

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

Apply radical rule:

a^{2} = a,

assuming

a \geq 0

(x^{3} + x^{2} + 1)^{2} = x^{3} + x^{2} + 1

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

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

\int t - 1 d t

\int \frac{sin ( x )}{5 cos ( x ) + 10} d x

\frac{\partial}{\partial x} (\frac{x}{x - y})

\int \frac{- y}{( x ^{2} + y ^{2} ) ^{2}} d y

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What is 8/(sqrt((x^3+x^2+1)^3)) ?
The solution to 8/(sqrt((x^3+x^2+1)^3)) is 8/(sqrt(x^3+x^2+1)(x^3+x^2+1))