3.97.88 \(\int (1-e^3+20 x+75 x^2) \, dx\)

Optimal. Leaf size=15 \[ x \left (-e^3+(1+5 x)^2\right ) \]

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Rubi [A]  time = 0.01, antiderivative size = 20, normalized size of antiderivative = 1.33, number of steps used = 1, number of rules used = 0, integrand size = 15, \(\frac {\text {number of rules}}{\text {integrand size}}\) = 0.000, Rules used = {} \begin {gather*} 25 x^3+10 x^2+\left (1-e^3\right ) x \end {gather*}

Antiderivative was successfully verified.

[In]

Int[1 - E^3 + 20*x + 75*x^2,x]

[Out]

(1 - E^3)*x + 10*x^2 + 25*x^3

Rubi steps

\begin {gather*} \begin {aligned} \text {integral} &=\left (1-e^3\right ) x+10 x^2+25 x^3\\ \end {aligned} \end {gather*}

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Mathematica [A]  time = 0.00, size = 18, normalized size = 1.20 \begin {gather*} x-e^3 x+10 x^2+25 x^3 \end {gather*}

Antiderivative was successfully verified.

[In]

Integrate[1 - E^3 + 20*x + 75*x^2,x]

[Out]

x - E^3*x + 10*x^2 + 25*x^3

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fricas [A]  time = 0.95, size = 17, normalized size = 1.13 \begin {gather*} 25 \, x^{3} + 10 \, x^{2} - x e^{3} + x \end {gather*}

Verification of antiderivative is not currently implemented for this CAS.

[In]

integrate(-exp(3)+75*x^2+20*x+1,x, algorithm="fricas")

[Out]

25*x^3 + 10*x^2 - x*e^3 + x

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giac [A]  time = 0.12, size = 17, normalized size = 1.13 \begin {gather*} 25 \, x^{3} + 10 \, x^{2} - x e^{3} + x \end {gather*}

Verification of antiderivative is not currently implemented for this CAS.

[In]

integrate(-exp(3)+75*x^2+20*x+1,x, algorithm="giac")

[Out]

25*x^3 + 10*x^2 - x*e^3 + x

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maple [A]  time = 0.02, size = 16, normalized size = 1.07

method	result	size
gosper	\(-x \left (-25 x^{2}+{\mathrm e}^{3}-10 x -1\right )\)	\(16\)
default	\(-x \,{\mathrm e}^{3}+25 x^{3}+10 x^{2}+x\)	\(18\)
risch	\(-x \,{\mathrm e}^{3}+25 x^{3}+10 x^{2}+x\)	\(18\)
norman	\(\left (-{\mathrm e}^{3}+1\right ) x +10 x^{2}+25 x^{3}\)	\(20\)

Verification of antiderivative is not currently implemented for this CAS.

[In]

int(-exp(3)+75*x^2+20*x+1,x,method=_RETURNVERBOSE)

[Out]

-x*(-25*x^2+exp(3)-10*x-1)

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maxima [A]  time = 0.37, size = 17, normalized size = 1.13 \begin {gather*} 25 \, x^{3} + 10 \, x^{2} - x e^{3} + x \end {gather*}

Verification of antiderivative is not currently implemented for this CAS.

[In]

integrate(-exp(3)+75*x^2+20*x+1,x, algorithm="maxima")

[Out]

25*x^3 + 10*x^2 - x*e^3 + x

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mupad [B]  time = 0.03, size = 18, normalized size = 1.20 \begin {gather*} 25\,x^3+10\,x^2+\left (1-{\mathrm {e}}^3\right )\,x \end {gather*}

Verification of antiderivative is not currently implemented for this CAS.

[In]

int(20*x - exp(3) + 75*x^2 + 1,x)

[Out]

10*x^2 - x*(exp(3) - 1) + 25*x^3

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sympy [A]  time = 0.05, size = 15, normalized size = 1.00 \begin {gather*} 25 x^{3} + 10 x^{2} + x \left (1 - e^{3}\right ) \end {gather*}

Verification of antiderivative is not currently implemented for this CAS.

[In]

integrate(-exp(3)+75*x**2+20*x+1,x)

[Out]

25*x**3 + 10*x**2 + x*(1 - exp(3))

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