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

The solution to x^2(3x+1/(x^3)) is (3x^4+1)/x

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

simplify

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

\frac{3 x ^{4} + 1}{x}

Solution steps

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

Join

3 x + \frac{1}{x ^{3}} : \frac{3 x ^{4} + 1}{x ^{3}}

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

Apply the fraction rule:

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

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

Apply exponent rule:

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

x^{3} = x^{2} x

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

Cancel the common factor:

x^{2}

= \frac{3 x ^{4} + 1}{x}

(1 + sec (a)) (1 - sec (a))

, 5 (3 - x) e^{x}

(5 + 5 x)^{2}

(2 - \frac{3}{x})^{6}

(x - 4 - 3) (x - 4 + 3)