3.59.15 \(\int (25+20 x+3 x^2+e (30+6 x)+e (-10-2 x) \log (4)) \, dx\)

Optimal. Leaf size=15 \[ (5+x)^2 (x-e (-3+\log (4))) \]

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Rubi [A]  time = 0.01, antiderivative size = 30, normalized size of antiderivative = 2.00, number of steps used = 1, number of rules used = 0, integrand size = 26, \(\frac {\text {number of rules}}{\text {integrand size}}\) = 0.000, Rules used = {} \begin {gather*} x^3+10 x^2+25 x+3 e (x+5)^2-e (x+5)^2 \log (4) \end {gather*}

Antiderivative was successfully verified.

[In]

Int[25 + 20*x + 3*x^2 + E*(30 + 6*x) + E*(-10 - 2*x)*Log[4],x]

[Out]

25*x + 10*x^2 + x^3 + 3*E*(5 + x)^2 - E*(5 + x)^2*Log[4]

Rubi steps

\begin {gather*} \begin {aligned} \text {integral} &=25 x+10 x^2+x^3+3 e (5+x)^2-e (5+x)^2 \log (4)\\ \end {aligned} \end {gather*}

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Mathematica [A]  time = 0.01, size = 18, normalized size = 1.20 \begin {gather*} x \left ((5+x)^2-e (10+x) (-3+\log (4))\right ) \end {gather*}

Antiderivative was successfully verified.

[In]

Integrate[25 + 20*x + 3*x^2 + E*(30 + 6*x) + E*(-10 - 2*x)*Log[4],x]

[Out]

x*((5 + x)^2 - E*(10 + x)*(-3 + Log[4]))

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fricas [A]  time = 0.50, size = 36, normalized size = 2.40 \begin {gather*} x^{3} - 2 \, {\left (x^{2} + 10 \, x\right )} e \log \relax (2) + 10 \, x^{2} + 3 \, {\left (x^{2} + 10 \, x\right )} e + 25 \, x \end {gather*}

Verification of antiderivative is not currently implemented for this CAS.

[In]

integrate(2*(-2*x-10)*exp(1)*log(2)+(6*x+30)*exp(1)+3*x^2+20*x+25,x, algorithm="fricas")

[Out]

x^3 - 2*(x^2 + 10*x)*e*log(2) + 10*x^2 + 3*(x^2 + 10*x)*e + 25*x

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giac [A]  time = 0.26, size = 36, normalized size = 2.40 \begin {gather*} x^{3} - 2 \, {\left (x^{2} + 10 \, x\right )} e \log \relax (2) + 10 \, x^{2} + 3 \, {\left (x^{2} + 10 \, x\right )} e + 25 \, x \end {gather*}

Verification of antiderivative is not currently implemented for this CAS.

[In]

integrate(2*(-2*x-10)*exp(1)*log(2)+(6*x+30)*exp(1)+3*x^2+20*x+25,x, algorithm="giac")

[Out]

x^3 - 2*(x^2 + 10*x)*e*log(2) + 10*x^2 + 3*(x^2 + 10*x)*e + 25*x

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maple [A]  time = 0.04, size = 35, normalized size = 2.33

method	result	size
norman	\(x^{3}+\left (-20 \,{\mathrm e} \ln \relax (2)+30 \,{\mathrm e}+25\right ) x +\left (-2 \,{\mathrm e} \ln \relax (2)+3 \,{\mathrm e}+10\right ) x^{2}\)	\(35\)
gosper	\(-x \left (2 x \,{\mathrm e} \ln \relax (2)+20 \,{\mathrm e} \ln \relax (2)-3 x \,{\mathrm e}-x^{2}-30 \,{\mathrm e}-10 x -25\right )\)	\(36\)
default	\(2 \,{\mathrm e} \ln \relax (2) \left (-x^{2}-10 x \right )+{\mathrm e} \left (3 x^{2}+30 x \right )+x^{3}+10 x^{2}+25 x\)	\(40\)
risch	\(-2 \,{\mathrm e} \ln \relax (2) x^{2}-20 x \,{\mathrm e} \ln \relax (2)+3 x^{2} {\mathrm e}+30 x \,{\mathrm e}+x^{3}+10 x^{2}+25 x\)	\(41\)

Verification of antiderivative is not currently implemented for this CAS.

[In]

int(2*(-2*x-10)*exp(1)*ln(2)+(6*x+30)*exp(1)+3*x^2+20*x+25,x,method=_RETURNVERBOSE)

[Out]

x^3+(-20*exp(1)*ln(2)+30*exp(1)+25)*x+(-2*exp(1)*ln(2)+3*exp(1)+10)*x^2

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maxima [A]  time = 0.36, size = 36, normalized size = 2.40 \begin {gather*} x^{3} - 2 \, {\left (x^{2} + 10 \, x\right )} e \log \relax (2) + 10 \, x^{2} + 3 \, {\left (x^{2} + 10 \, x\right )} e + 25 \, x \end {gather*}

Verification of antiderivative is not currently implemented for this CAS.

[In]

integrate(2*(-2*x-10)*exp(1)*log(2)+(6*x+30)*exp(1)+3*x^2+20*x+25,x, algorithm="maxima")

[Out]

x^3 - 2*(x^2 + 10*x)*e*log(2) + 10*x^2 + 3*(x^2 + 10*x)*e + 25*x

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mupad [B]  time = 0.06, size = 34, normalized size = 2.27 \begin {gather*} x^3+\left (3\,\mathrm {e}-2\,\mathrm {e}\,\ln \relax (2)+10\right )\,x^2+\left (30\,\mathrm {e}-20\,\mathrm {e}\,\ln \relax (2)+25\right )\,x \end {gather*}

Verification of antiderivative is not currently implemented for this CAS.

[In]

int(20*x + 3*x^2 + exp(1)*(6*x + 30) - 2*exp(1)*log(2)*(2*x + 10) + 25,x)

[Out]

x*(30*exp(1) - 20*exp(1)*log(2) + 25) + x^2*(3*exp(1) - 2*exp(1)*log(2) + 10) + x^3

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sympy [B]  time = 0.06, size = 37, normalized size = 2.47 \begin {gather*} x^{3} + x^{2} \left (- 2 e \log {\relax (2 )} + 3 e + 10\right ) + x \left (- 20 e \log {\relax (2 )} + 25 + 30 e\right ) \end {gather*}

Verification of antiderivative is not currently implemented for this CAS.

[In]

integrate(2*(-2*x-10)*exp(1)*ln(2)+(6*x+30)*exp(1)+3*x**2+20*x+25,x)

[Out]

x**3 + x**2*(-2*E*log(2) + 3*E + 10) + x*(-20*E*log(2) + 25 + 30*E)

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