3.97.24 \(\int \frac {-1600+x^3}{x^3} \, dx\)

Optimal. Leaf size=13 \[ -25+\log \left (e^{-20+\frac {800}{x^2}+x}\right ) \]

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Rubi [A]  time = 0.00, antiderivative size = 7, normalized size of antiderivative = 0.54, number of steps used = 2, number of rules used = 1, integrand size = 9, \(\frac {\text {number of rules}}{\text {integrand size}}\) = 0.111, Rules used = {14} \begin {gather*} \frac {800}{x^2}+x \end {gather*}

Antiderivative was successfully verified.

[In]

Int[(-1600 + x^3)/x^3,x]

[Out]

800/x^2 + x

Rule 14

Int[(u_)*((c_.)*(x_))^(m_.), x_Symbol] :> Int[ExpandIntegrand[(c*x)^m*u, x], x] /; FreeQ[{c, m}, x] && SumQ[u]
&&  !LinearQ[u, x] &&  !MatchQ[u, (a_) + (b_.)*(v_) /; FreeQ[{a, b}, x] && InverseFunctionQ[v]]

Rubi steps

\begin {gather*} \begin {aligned} \text {integral} &=\int \left (1-\frac {1600}{x^3}\right ) \, dx\\ &=\frac {800}{x^2}+x\\ \end {aligned} \end {gather*}

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Mathematica [A]  time = 0.00, size = 7, normalized size = 0.54 \begin {gather*} \frac {800}{x^2}+x \end {gather*}

Antiderivative was successfully verified.

[In]

Integrate[(-1600 + x^3)/x^3,x]

[Out]

800/x^2 + x

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fricas [A]  time = 0.47, size = 9, normalized size = 0.69 \begin {gather*} \frac {x^{3} + 800}{x^{2}} \end {gather*}

Verification of antiderivative is not currently implemented for this CAS.

[In]

integrate((x^3-1600)/x^3,x, algorithm="fricas")

[Out]

(x^3 + 800)/x^2

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giac [A]  time = 0.19, size = 7, normalized size = 0.54 \begin {gather*} x + \frac {800}{x^{2}} \end {gather*}

Verification of antiderivative is not currently implemented for this CAS.

[In]

integrate((x^3-1600)/x^3,x, algorithm="giac")

[Out]

x + 800/x^2

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maple [A]  time = 0.02, size = 8, normalized size = 0.62

method	result	size
default	\(x +\frac {800}{x^{2}}\)	\(8\)
risch	\(x +\frac {800}{x^{2}}\)	\(8\)
gosper	\(\frac {x^{3}+800}{x^{2}}\)	\(10\)
norman	\(\frac {x^{3}+800}{x^{2}}\)	\(10\)

Verification of antiderivative is not currently implemented for this CAS.

[In]

int((x^3-1600)/x^3,x,method=_RETURNVERBOSE)

[Out]

x+800/x^2

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maxima [A]  time = 0.35, size = 7, normalized size = 0.54 \begin {gather*} x + \frac {800}{x^{2}} \end {gather*}

Verification of antiderivative is not currently implemented for this CAS.

[In]

integrate((x^3-1600)/x^3,x, algorithm="maxima")

[Out]

x + 800/x^2

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mupad [B]  time = 0.02, size = 7, normalized size = 0.54 \begin {gather*} x+\frac {800}{x^2} \end {gather*}

Verification of antiderivative is not currently implemented for this CAS.

[In]

int((x^3 - 1600)/x^3,x)

[Out]

x + 800/x^2

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sympy [A]  time = 0.06, size = 5, normalized size = 0.38 \begin {gather*} x + \frac {800}{x^{2}} \end {gather*}

Verification of antiderivative is not currently implemented for this CAS.

[In]

integrate((x**3-1600)/x**3,x)

[Out]

x + 800/x**2

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