3.20.85 \(\int \frac {e^5-2 x^3}{x^2} \, dx\)

Optimal. Leaf size=15 \[ -2-\frac {e^5}{x}-x^2 \]

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Rubi [A]  time = 0.01, antiderivative size = 14, normalized size of antiderivative = 0.93, number of steps used = 2, number of rules used = 1, integrand size = 13, \(\frac {\text {number of rules}}{\text {integrand size}}\) = 0.077, Rules used = {14} \begin {gather*} -x^2-\frac {e^5}{x} \end {gather*}

Antiderivative was successfully verified.

[In]

Int[(E^5 - 2*x^3)/x^2,x]

[Out]

-(E^5/x) - x^2

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 (\frac {e^5}{x^2}-2 x\right ) \, dx\\ &=-\frac {e^5}{x}-x^2\\ \end {aligned} \end {gather*}

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Mathematica [A]  time = 0.00, size = 14, normalized size = 0.93 \begin {gather*} -\frac {e^5}{x}-x^2 \end {gather*}

Antiderivative was successfully verified.

[In]

Integrate[(E^5 - 2*x^3)/x^2,x]

[Out]

-(E^5/x) - x^2

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fricas [A]  time = 0.56, size = 11, normalized size = 0.73 \begin {gather*} -\frac {x^{3} + e^{5}}{x} \end {gather*}

Verification of antiderivative is not currently implemented for this CAS.

[In]

integrate((exp(5)-2*x^3)/x^2,x, algorithm="fricas")

[Out]

-(x^3 + e^5)/x

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giac [A]  time = 0.27, size = 13, normalized size = 0.87 \begin {gather*} -x^{2} - \frac {e^{5}}{x} \end {gather*}

Verification of antiderivative is not currently implemented for this CAS.

[In]

integrate((exp(5)-2*x^3)/x^2,x, algorithm="giac")

[Out]

-x^2 - e^5/x

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maple [A]  time = 0.03, size = 12, normalized size = 0.80

method	result	size
gosper	\(-\frac {{\mathrm e}^{5}+x^{3}}{x}\)	\(12\)
default	\(-x^{2}-\frac {{\mathrm e}^{5}}{x}\)	\(14\)
risch	\(-x^{2}-\frac {{\mathrm e}^{5}}{x}\)	\(14\)
norman	\(\frac {-x^{3}-{\mathrm e}^{5}}{x}\)	\(15\)

Verification of antiderivative is not currently implemented for this CAS.

[In]

int((exp(5)-2*x^3)/x^2,x,method=_RETURNVERBOSE)

[Out]

-(exp(5)+x^3)/x

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maxima [A]  time = 0.50, size = 13, normalized size = 0.87 \begin {gather*} -x^{2} - \frac {e^{5}}{x} \end {gather*}

Verification of antiderivative is not currently implemented for this CAS.

[In]

integrate((exp(5)-2*x^3)/x^2,x, algorithm="maxima")

[Out]

-x^2 - e^5/x

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mupad [B]  time = 0.03, size = 11, normalized size = 0.73 \begin {gather*} -\frac {x^3+{\mathrm {e}}^5}{x} \end {gather*}

Verification of antiderivative is not currently implemented for this CAS.

[In]

int((exp(5) - 2*x^3)/x^2,x)

[Out]

-(exp(5) + x^3)/x

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sympy [A]  time = 0.07, size = 8, normalized size = 0.53 \begin {gather*} - x^{2} - \frac {e^{5}}{x} \end {gather*}

Verification of antiderivative is not currently implemented for this CAS.

[In]

integrate((exp(5)-2*x**3)/x**2,x)

[Out]

-x**2 - exp(5)/x

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