3.10.95 \(\int (6-6 x-3 x^2+e^2 (3+2 x)+(-3-2 x) \log ^2(5)) \, dx\)

Optimal. Leaf size=22 \[ x+x \left (5-(3+x) \left (-e^2+x+\log ^2(5)\right )\right ) \]

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Rubi [A]  time = 0.02, antiderivative size = 43, normalized size of antiderivative = 1.95, number of steps used = 1, number of rules used = 0, integrand size = 29, \(\frac {\text {number of rules}}{\text {integrand size}}\) = 0.000, Rules used = {} \begin {gather*} -x^3-3 x^2+6 x+\frac {1}{4} e^2 (2 x+3)^2-\frac {1}{4} (2 x+3)^2 \log ^2(5) \end {gather*}

Antiderivative was successfully verified.

[In]

Int[6 - 6*x - 3*x^2 + E^2*(3 + 2*x) + (-3 - 2*x)*Log[5]^2,x]

[Out]

6*x - 3*x^2 - x^3 + (E^2*(3 + 2*x)^2)/4 - ((3 + 2*x)^2*Log[5]^2)/4

Rubi steps

\begin {gather*} \begin {aligned} \text {integral} &=6 x-3 x^2-x^3+\frac {1}{4} e^2 (3+2 x)^2-\frac {1}{4} (3+2 x)^2 \log ^2(5)\\ \end {aligned} \end {gather*}

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Mathematica [A]  time = 0.01, size = 43, normalized size = 1.95 \begin {gather*} 6 x+3 e^2 x-3 x^2+e^2 x^2-x^3-3 x \log ^2(5)-x^2 \log ^2(5) \end {gather*}

Antiderivative was successfully verified.

[In]

Integrate[6 - 6*x - 3*x^2 + E^2*(3 + 2*x) + (-3 - 2*x)*Log[5]^2,x]

[Out]

6*x + 3*E^2*x - 3*x^2 + E^2*x^2 - x^3 - 3*x*Log[5]^2 - x^2*Log[5]^2

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fricas [A]  time = 0.66, size = 37, normalized size = 1.68 \begin {gather*} -x^{3} - {\left (x^{2} + 3 \, x\right )} \log \relax (5)^{2} - 3 \, x^{2} + {\left (x^{2} + 3 \, x\right )} e^{2} + 6 \, x \end {gather*}

Verification of antiderivative is not currently implemented for this CAS.

[In]

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

[Out]

-x^3 - (x^2 + 3*x)*log(5)^2 - 3*x^2 + (x^2 + 3*x)*e^2 + 6*x

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giac [A]  time = 0.29, size = 37, normalized size = 1.68 \begin {gather*} -x^{3} - {\left (x^{2} + 3 \, x\right )} \log \relax (5)^{2} - 3 \, x^{2} + {\left (x^{2} + 3 \, x\right )} e^{2} + 6 \, x \end {gather*}

Verification of antiderivative is not currently implemented for this CAS.

[In]

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

[Out]

-x^3 - (x^2 + 3*x)*log(5)^2 - 3*x^2 + (x^2 + 3*x)*e^2 + 6*x

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maple [A]  time = 0.02, size = 34, normalized size = 1.55

method	result	size
gosper	\(x \left (-x \ln \relax (5)^{2}+{\mathrm e}^{2} x -3 \ln \relax (5)^{2}-x^{2}+3 \,{\mathrm e}^{2}-3 x +6\right )\)	\(34\)
norman	\(-x^{3}+\left (-\ln \relax (5)^{2}+{\mathrm e}^{2}-3\right ) x^{2}+\left (-3 \ln \relax (5)^{2}+3 \,{\mathrm e}^{2}+6\right ) x\)	\(35\)
default	\(\ln \relax (5)^{2} \left (-x^{2}-3 x \right )+{\mathrm e}^{2} \left (x^{2}+3 x \right )-x^{3}-3 x^{2}+6 x\)	\(39\)
risch	\(-x^{2} \ln \relax (5)^{2}-3 x \ln \relax (5)^{2}+x^{2} {\mathrm e}^{2}+3 \,{\mathrm e}^{2} x -x^{3}-3 x^{2}+6 x\)	\(42\)

Verification of antiderivative is not currently implemented for this CAS.

[In]

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

[Out]

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

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maxima [A]  time = 0.46, size = 37, normalized size = 1.68 \begin {gather*} -x^{3} - {\left (x^{2} + 3 \, x\right )} \log \relax (5)^{2} - 3 \, x^{2} + {\left (x^{2} + 3 \, x\right )} e^{2} + 6 \, x \end {gather*}

Verification of antiderivative is not currently implemented for this CAS.

[In]

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

[Out]

-x^3 - (x^2 + 3*x)*log(5)^2 - 3*x^2 + (x^2 + 3*x)*e^2 + 6*x

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mupad [B]  time = 0.05, size = 35, normalized size = 1.59 \begin {gather*} -x^3+\left ({\mathrm {e}}^2-{\ln \relax (5)}^2-3\right )\,x^2+\left (3\,{\mathrm {e}}^2-3\,{\ln \relax (5)}^2+6\right )\,x \end {gather*}

Verification of antiderivative is not currently implemented for this CAS.

[In]

int(exp(2)*(2*x + 3) - log(5)^2*(2*x + 3) - 3*x^2 - 6*x + 6,x)

[Out]

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

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sympy [A]  time = 0.06, size = 31, normalized size = 1.41 \begin {gather*} - x^{3} + x^{2} \left (-3 - \log {\relax (5 )}^{2} + e^{2}\right ) + x \left (- 3 \log {\relax (5 )}^{2} + 6 + 3 e^{2}\right ) \end {gather*}

Verification of antiderivative is not currently implemented for this CAS.

[In]

integrate((-2*x-3)*ln(5)**2+(2*x+3)*exp(2)-3*x**2-6*x+6,x)

[Out]

-x**3 + x**2*(-3 - log(5)**2 + exp(2)) + x*(-3*log(5)**2 + 6 + 3*exp(2))

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