3.84.50 \(\int (33+e^{18} (-8-4 x)-2 x+24 x^2+4 x^3+60 x^5-10 x^9) \, dx\)

Optimal. Leaf size=29 \[ x-x^2 \left (5-x^4\right )^2+\left (-e^{18}+(2+x)^2\right )^2 \]

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Rubi [A]  time = 0.01, antiderivative size = 37, normalized size of antiderivative = 1.28, number of steps used = 1, number of rules used = 0, integrand size = 34, \(\frac {\text {number of rules}}{\text {integrand size}}\) = 0.000, Rules used = {} \begin {gather*} -x^{10}+10 x^6+x^4+8 x^3-x^2+33 x-2 e^{18} (x+2)^2 \end {gather*}

Antiderivative was successfully verified.

[In]

Int[33 + E^18*(-8 - 4*x) - 2*x + 24*x^2 + 4*x^3 + 60*x^5 - 10*x^9,x]

[Out]

33*x - x^2 + 8*x^3 + x^4 + 10*x^6 - x^10 - 2*E^18*(2 + x)^2

Rubi steps

\begin {gather*} \begin {aligned} \text {integral} &=33 x-x^2+8 x^3+x^4+10 x^6-x^{10}-2 e^{18} (2+x)^2\\ \end {aligned} \end {gather*}

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Mathematica [A]  time = 0.00, size = 41, normalized size = 1.41 \begin {gather*} 33 x-8 e^{18} x-x^2-2 e^{18} x^2+8 x^3+x^4+10 x^6-x^{10} \end {gather*}

Antiderivative was successfully verified.

[In]

Integrate[33 + E^18*(-8 - 4*x) - 2*x + 24*x^2 + 4*x^3 + 60*x^5 - 10*x^9,x]

[Out]

33*x - 8*E^18*x - x^2 - 2*E^18*x^2 + 8*x^3 + x^4 + 10*x^6 - x^10

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fricas [A]  time = 0.90, size = 38, normalized size = 1.31 \begin {gather*} -x^{10} + 10 \, x^{6} + x^{4} + 8 \, x^{3} - x^{2} - 2 \, {\left (x^{2} + 4 \, x\right )} e^{18} + 33 \, x \end {gather*}

Verification of antiderivative is not currently implemented for this CAS.

[In]

integrate((-4*x-8)*exp(9)^2-10*x^9+60*x^5+4*x^3+24*x^2-2*x+33,x, algorithm="fricas")

[Out]

-x^10 + 10*x^6 + x^4 + 8*x^3 - x^2 - 2*(x^2 + 4*x)*e^18 + 33*x

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giac [A]  time = 0.14, size = 38, normalized size = 1.31 \begin {gather*} -x^{10} + 10 \, x^{6} + x^{4} + 8 \, x^{3} - x^{2} - 2 \, {\left (x^{2} + 4 \, x\right )} e^{18} + 33 \, x \end {gather*}

Verification of antiderivative is not currently implemented for this CAS.

[In]

integrate((-4*x-8)*exp(9)^2-10*x^9+60*x^5+4*x^3+24*x^2-2*x+33,x, algorithm="giac")

[Out]

-x^10 + 10*x^6 + x^4 + 8*x^3 - x^2 - 2*(x^2 + 4*x)*e^18 + 33*x

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maple [A]  time = 0.04, size = 38, normalized size = 1.31

method	result	size
gosper	\(-x \left (x^{9}-10 x^{5}+2 \,{\mathrm e}^{18} x -x^{3}+8 \,{\mathrm e}^{18}-8 x^{2}+x -33\right )\)	\(38\)
risch	\(-2 x^{2} {\mathrm e}^{18}-8 \,{\mathrm e}^{18} x -x^{10}+10 x^{6}+x^{4}+8 x^{3}-x^{2}+33 x\)	\(40\)
default	\({\mathrm e}^{18} \left (-2 x^{2}-8 x \right )-x^{10}+10 x^{6}+x^{4}+8 x^{3}-x^{2}+33 x\)	\(42\)
norman	\(x^{4}+\left (-8 \,{\mathrm e}^{18}+33\right ) x +\left (-2 \,{\mathrm e}^{18}-1\right ) x^{2}+8 x^{3}+10 x^{6}-x^{10}\)	\(42\)

Verification of antiderivative is not currently implemented for this CAS.

[In]

int((-4*x-8)*exp(9)^2-10*x^9+60*x^5+4*x^3+24*x^2-2*x+33,x,method=_RETURNVERBOSE)

[Out]

-x*(x^9-10*x^5+2*exp(9)^2*x-x^3+8*exp(9)^2-8*x^2+x-33)

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maxima [A]  time = 0.36, size = 38, normalized size = 1.31 \begin {gather*} -x^{10} + 10 \, x^{6} + x^{4} + 8 \, x^{3} - x^{2} - 2 \, {\left (x^{2} + 4 \, x\right )} e^{18} + 33 \, x \end {gather*}

Verification of antiderivative is not currently implemented for this CAS.

[In]

integrate((-4*x-8)*exp(9)^2-10*x^9+60*x^5+4*x^3+24*x^2-2*x+33,x, algorithm="maxima")

[Out]

-x^10 + 10*x^6 + x^4 + 8*x^3 - x^2 - 2*(x^2 + 4*x)*e^18 + 33*x

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mupad [B]  time = 5.42, size = 39, normalized size = 1.34 \begin {gather*} -x^{10}+10\,x^6+x^4+8\,x^3+\left (-2\,{\mathrm {e}}^{18}-1\right )\,x^2+\left (33-8\,{\mathrm {e}}^{18}\right )\,x \end {gather*}

Verification of antiderivative is not currently implemented for this CAS.

[In]

int(24*x^2 - 2*x + 4*x^3 + 60*x^5 - 10*x^9 - exp(18)*(4*x + 8) + 33,x)

[Out]

8*x^3 - x^2*(2*exp(18) + 1) + x^4 + 10*x^6 - x^10 - x*(8*exp(18) - 33)

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sympy [A]  time = 0.06, size = 36, normalized size = 1.24 \begin {gather*} - x^{10} + 10 x^{6} + x^{4} + 8 x^{3} + x^{2} \left (- 2 e^{18} - 1\right ) + x \left (33 - 8 e^{18}\right ) \end {gather*}

Verification of antiderivative is not currently implemented for this CAS.

[In]

integrate((-4*x-8)*exp(9)**2-10*x**9+60*x**5+4*x**3+24*x**2-2*x+33,x)

[Out]

-x**10 + 10*x**6 + x**4 + 8*x**3 + x**2*(-2*exp(18) - 1) + x*(33 - 8*exp(18))

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