3.4.57 \(\int (-7+4 x-5 e^6 x^4) \, dx\)

Optimal. Leaf size=17 \[ 2+x+2 (-4+x) x-e^6 x^5 \]

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Rubi [A]  time = 0.00, antiderivative size = 17, normalized size of antiderivative = 1.00, number of steps used = 1, number of rules used = 0, integrand size = 13, \(\frac {\text {number of rules}}{\text {integrand size}}\) = 0.000, Rules used = {} \begin {gather*} -e^6 x^5+2 x^2-7 x \end {gather*}

Antiderivative was successfully verified.

[In]

Int[-7 + 4*x - 5*E^6*x^4,x]

[Out]

-7*x + 2*x^2 - E^6*x^5

Rubi steps

\begin {gather*} \begin {aligned} \text {integral} &=-7 x+2 x^2-e^6 x^5\\ \end {aligned} \end {gather*}

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Mathematica [A]  time = 0.00, size = 17, normalized size = 1.00 \begin {gather*} -7 x+2 x^2-e^6 x^5 \end {gather*}

Antiderivative was successfully verified.

[In]

Integrate[-7 + 4*x - 5*E^6*x^4,x]

[Out]

-7*x + 2*x^2 - E^6*x^5

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fricas [A]  time = 0.85, size = 16, normalized size = 0.94 \begin {gather*} -x^{5} e^{6} + 2 \, x^{2} - 7 \, x \end {gather*}

Verification of antiderivative is not currently implemented for this CAS.

[In]

integrate(-5*x^2*exp(3+log(x))^2+4*x-7,x, algorithm="fricas")

[Out]

-x^5*e^6 + 2*x^2 - 7*x

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giac [A]  time = 0.60, size = 16, normalized size = 0.94 \begin {gather*} -x^{5} e^{6} + 2 \, x^{2} - 7 \, x \end {gather*}

Verification of antiderivative is not currently implemented for this CAS.

[In]

integrate(-5*x^2*exp(3+log(x))^2+4*x-7,x, algorithm="giac")

[Out]

-x^5*e^6 + 2*x^2 - 7*x

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maple [A]  time = 0.02, size = 17, normalized size = 1.00

method	result	size
default	\(2 x^{2}-7 x -x^{5} {\mathrm e}^{6}\)	\(17\)
risch	\(2 x^{2}-7 x -x^{5} {\mathrm e}^{6}\)	\(17\)
norman	\(2 x^{2}-7 x -x^{5} {\mathrm e}^{6}\)	\(19\)

Verification of antiderivative is not currently implemented for this CAS.

[In]

int(-5*x^2*exp(3+ln(x))^2+4*x-7,x,method=_RETURNVERBOSE)

[Out]

2*x^2-7*x-x^5*exp(6)

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maxima [A]  time = 0.45, size = 16, normalized size = 0.94 \begin {gather*} -x^{5} e^{6} + 2 \, x^{2} - 7 \, x \end {gather*}

Verification of antiderivative is not currently implemented for this CAS.

[In]

integrate(-5*x^2*exp(3+log(x))^2+4*x-7,x, algorithm="maxima")

[Out]

-x^5*e^6 + 2*x^2 - 7*x

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mupad [B]  time = 0.35, size = 14, normalized size = 0.82 \begin {gather*} -x\,\left ({\mathrm {e}}^6\,x^4-2\,x+7\right ) \end {gather*}

Verification of antiderivative is not currently implemented for this CAS.

[In]

int(4*x - 5*x^2*exp(2*log(x) + 6) - 7,x)

[Out]

-x*(x^4*exp(6) - 2*x + 7)

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sympy [A]  time = 0.05, size = 14, normalized size = 0.82 \begin {gather*} - x^{5} e^{6} + 2 x^{2} - 7 x \end {gather*}

Verification of antiderivative is not currently implemented for this CAS.

[In]

integrate(-5*x**2*exp(3+ln(x))**2+4*x-7,x)

[Out]

-x**5*exp(6) + 2*x**2 - 7*x

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