3.32.12 \(\int \frac {1}{4} e^9 (625 x^3+6250 x^4+15000 x^5) \, dx\)

Optimal. Leaf size=19 \[ \frac {1}{e^4}+625 e^9 x^4 \left (\frac {1}{4}+x\right )^2 \]

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Rubi [A]  time = 0.01, antiderivative size = 29, normalized size of antiderivative = 1.53, number of steps used = 2, number of rules used = 1, integrand size = 23, \(\frac {\text {number of rules}}{\text {integrand size}}\) = 0.043, Rules used = {12} \begin {gather*} 625 e^9 x^6+\frac {625 e^9 x^5}{2}+\frac {625 e^9 x^4}{16} \end {gather*}

Antiderivative was successfully verified.

[In]

Int[(E^9*(625*x^3 + 6250*x^4 + 15000*x^5))/4,x]

[Out]

(625*E^9*x^4)/16 + (625*E^9*x^5)/2 + 625*E^9*x^6

Rule 12

Int[(a_)*(u_), x_Symbol] :> Dist[a, Int[u, x], x] /; FreeQ[a, x] &&  !MatchQ[u, (b_)*(v_) /; FreeQ[b, x]]

Rubi steps

\begin {gather*} \begin {aligned} \text {integral} &=\frac {1}{4} e^9 \int \left (625 x^3+6250 x^4+15000 x^5\right ) \, dx\\ &=\frac {625 e^9 x^4}{16}+\frac {625 e^9 x^5}{2}+625 e^9 x^6\\ \end {aligned} \end {gather*}

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Mathematica [A]  time = 0.00, size = 25, normalized size = 1.32 \begin {gather*} \frac {625}{4} e^9 \left (\frac {x^4}{4}+2 x^5+4 x^6\right ) \end {gather*}

Antiderivative was successfully verified.

[In]

Integrate[(E^9*(625*x^3 + 6250*x^4 + 15000*x^5))/4,x]

[Out]

(625*E^9*(x^4/4 + 2*x^5 + 4*x^6))/4

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fricas [A]  time = 0.66, size = 18, normalized size = 0.95 \begin {gather*} \frac {625}{16} \, {\left (16 \, x^{6} + 8 \, x^{5} + x^{4}\right )} e^{9} \end {gather*}

Verification of antiderivative is not currently implemented for this CAS.

[In]

integrate(1/4*(15000*x^5+6250*x^4+625*x^3)*exp(9),x, algorithm="fricas")

[Out]

625/16*(16*x^6 + 8*x^5 + x^4)*e^9

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giac [A]  time = 0.34, size = 18, normalized size = 0.95 \begin {gather*} \frac {625}{16} \, {\left (16 \, x^{6} + 8 \, x^{5} + x^{4}\right )} e^{9} \end {gather*}

Verification of antiderivative is not currently implemented for this CAS.

[In]

integrate(1/4*(15000*x^5+6250*x^4+625*x^3)*exp(9),x, algorithm="giac")

[Out]

625/16*(16*x^6 + 8*x^5 + x^4)*e^9

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maple [A]  time = 0.04, size = 15, normalized size = 0.79

method	result	size
gosper	\(\frac {625 x^{4} \left (4 x +1\right )^{2} {\mathrm e}^{9}}{16}\)	\(15\)
default	\(\frac {{\mathrm e}^{9} \left (2500 x^{6}+1250 x^{5}+\frac {625}{4} x^{4}\right )}{4}\)	\(21\)
norman	\(\frac {625 x^{4} {\mathrm e}^{9}}{16}+\frac {625 \,{\mathrm e}^{9} x^{5}}{2}+625 \,{\mathrm e}^{9} x^{6}\)	\(23\)
risch	\(\frac {625 x^{4} {\mathrm e}^{9}}{16}+\frac {625 \,{\mathrm e}^{9} x^{5}}{2}+625 \,{\mathrm e}^{9} x^{6}\)	\(23\)

Verification of antiderivative is not currently implemented for this CAS.

[In]

int(1/4*(15000*x^5+6250*x^4+625*x^3)*exp(9),x,method=_RETURNVERBOSE)

[Out]

625/16*x^4*(4*x+1)^2*exp(9)

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maxima [A]  time = 0.37, size = 18, normalized size = 0.95 \begin {gather*} \frac {625}{16} \, {\left (16 \, x^{6} + 8 \, x^{5} + x^{4}\right )} e^{9} \end {gather*}

Verification of antiderivative is not currently implemented for this CAS.

[In]

integrate(1/4*(15000*x^5+6250*x^4+625*x^3)*exp(9),x, algorithm="maxima")

[Out]

625/16*(16*x^6 + 8*x^5 + x^4)*e^9

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mupad [B]  time = 0.05, size = 14, normalized size = 0.74 \begin {gather*} \frac {625\,x^4\,{\mathrm {e}}^9\,{\left (4\,x+1\right )}^2}{16} \end {gather*}

Verification of antiderivative is not currently implemented for this CAS.

[In]

int((exp(9)*(625*x^3 + 6250*x^4 + 15000*x^5))/4,x)

[Out]

(625*x^4*exp(9)*(4*x + 1)^2)/16

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sympy [A]  time = 0.06, size = 27, normalized size = 1.42 \begin {gather*} 625 x^{6} e^{9} + \frac {625 x^{5} e^{9}}{2} + \frac {625 x^{4} e^{9}}{16} \end {gather*}

Verification of antiderivative is not currently implemented for this CAS.

[In]

integrate(1/4*(15000*x**5+6250*x**4+625*x**3)*exp(9),x)

[Out]

625*x**6*exp(9) + 625*x**5*exp(9)/2 + 625*x**4*exp(9)/16

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