3.70.44 \(\int (-e^{10}+8 e^5 x^3-7 x^6+e^4 (-3+2 x)) \, dx\)

Optimal. Leaf size=23 \[ x \left (e^4 (-3+x)-\left (-e^5+x^3\right )^2\right ) \]

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Rubi [A]  time = 0.02, antiderivative size = 34, normalized size of antiderivative = 1.48, number of steps used = 1, number of rules used = 0, integrand size = 28, \(\frac {\text {number of rules}}{\text {integrand size}}\) = 0.000, Rules used = {} \begin {gather*} -x^7+2 e^5 x^4-e^{10} x+\frac {1}{4} e^4 (3-2 x)^2 \end {gather*}

Antiderivative was successfully verified.

[In]

Int[-E^10 + 8*E^5*x^3 - 7*x^6 + E^4*(-3 + 2*x),x]

[Out]

(E^4*(3 - 2*x)^2)/4 - E^10*x + 2*E^5*x^4 - x^7

Rubi steps

\begin {gather*} \begin {aligned} \text {integral} &=\frac {1}{4} e^4 (3-2 x)^2-e^{10} x+2 e^5 x^4-x^7\\ \end {aligned} \end {gather*}

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Mathematica [A]  time = 0.00, size = 33, normalized size = 1.43 \begin {gather*} -3 e^4 x-e^{10} x+e^4 x^2+2 e^5 x^4-x^7 \end {gather*}

Antiderivative was successfully verified.

[In]

Integrate[-E^10 + 8*E^5*x^3 - 7*x^6 + E^4*(-3 + 2*x),x]

[Out]

-3*E^4*x - E^10*x + E^4*x^2 + 2*E^5*x^4 - x^7

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fricas [A]  time = 0.71, size = 28, normalized size = 1.22 \begin {gather*} -x^{7} + 2 \, x^{4} e^{5} - x e^{10} + {\left (x^{2} - 3 \, x\right )} e^{4} \end {gather*}

Verification of antiderivative is not currently implemented for this CAS.

[In]

integrate(-exp(5)^2+8*x^3*exp(5)+(2*x-3)*exp(4)-7*x^6,x, algorithm="fricas")

[Out]

-x^7 + 2*x^4*e^5 - x*e^10 + (x^2 - 3*x)*e^4

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giac [A]  time = 0.22, size = 28, normalized size = 1.22 \begin {gather*} -x^{7} + 2 \, x^{4} e^{5} - x e^{10} + {\left (x^{2} - 3 \, x\right )} e^{4} \end {gather*}

Verification of antiderivative is not currently implemented for this CAS.

[In]

integrate(-exp(5)^2+8*x^3*exp(5)+(2*x-3)*exp(4)-7*x^6,x, algorithm="giac")

[Out]

-x^7 + 2*x^4*e^5 - x*e^10 + (x^2 - 3*x)*e^4

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maple [A]  time = 0.02, size = 28, normalized size = 1.22

method	result	size
gosper	\(-x \left (x^{6}-2 x^{3} {\mathrm e}^{5}+{\mathrm e}^{10}-x \,{\mathrm e}^{4}+3 \,{\mathrm e}^{4}\right )\)	\(28\)
risch	\(-x \,{\mathrm e}^{10}+2 x^{4} {\mathrm e}^{5}+x^{2} {\mathrm e}^{4}-3 x \,{\mathrm e}^{4}-x^{7}\)	\(30\)
default	\(-x \,{\mathrm e}^{10}+2 x^{4} {\mathrm e}^{5}+{\mathrm e}^{4} \left (x^{2}-3 x \right )-x^{7}\)	\(31\)
norman	\(x^{2} {\mathrm e}^{4}+\left (-{\mathrm e}^{10}-3 \,{\mathrm e}^{4}\right ) x -x^{7}+2 x^{4} {\mathrm e}^{5}\)	\(33\)

Verification of antiderivative is not currently implemented for this CAS.

[In]

int(-exp(5)^2+8*x^3*exp(5)+(2*x-3)*exp(4)-7*x^6,x,method=_RETURNVERBOSE)

[Out]

-x*(x^6-2*x^3*exp(5)+exp(5)^2-x*exp(4)+3*exp(4))

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maxima [A]  time = 0.37, size = 28, normalized size = 1.22 \begin {gather*} -x^{7} + 2 \, x^{4} e^{5} - x e^{10} + {\left (x^{2} - 3 \, x\right )} e^{4} \end {gather*}

Verification of antiderivative is not currently implemented for this CAS.

[In]

integrate(-exp(5)^2+8*x^3*exp(5)+(2*x-3)*exp(4)-7*x^6,x, algorithm="maxima")

[Out]

-x^7 + 2*x^4*e^5 - x*e^10 + (x^2 - 3*x)*e^4

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mupad [B]  time = 4.15, size = 29, normalized size = 1.26 \begin {gather*} -x^7+2\,{\mathrm {e}}^5\,x^4+{\mathrm {e}}^4\,x^2+\left (-3\,{\mathrm {e}}^4-{\mathrm {e}}^{10}\right )\,x \end {gather*}

Verification of antiderivative is not currently implemented for this CAS.

[In]

int(8*x^3*exp(5) - exp(10) - 7*x^6 + exp(4)*(2*x - 3),x)

[Out]

x^2*exp(4) - x*(3*exp(4) + exp(10)) + 2*x^4*exp(5) - x^7

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sympy [A]  time = 0.06, size = 29, normalized size = 1.26 \begin {gather*} - x^{7} + 2 x^{4} e^{5} + x^{2} e^{4} + x \left (- e^{10} - 3 e^{4}\right ) \end {gather*}

Verification of antiderivative is not currently implemented for this CAS.

[In]

integrate(-exp(5)**2+8*x**3*exp(5)+(2*x-3)*exp(4)-7*x**6,x)

[Out]

-x**7 + 2*x**4*exp(5) + x**2*exp(4) + x*(-exp(10) - 3*exp(4))

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