3.4.25 \(\int (750 x-750 x^2+350 x^6-150 x^2 \log (2)) \, dx\)

Optimal. Leaf size=24 \[ 25 x^2 \left (5 (3-2 x)+2 x \left (x^4-\log (2)\right )\right ) \]

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Rubi [A]  time = 0.01, antiderivative size = 20, normalized size of antiderivative = 0.83, number of steps used = 2, number of rules used = 1, integrand size = 21, \(\frac {\text {number of rules}}{\text {integrand size}}\) = 0.048, Rules used = {6} \begin {gather*} 50 x^7-50 x^3 (5+\log (2))+375 x^2 \end {gather*}

Antiderivative was successfully verified.

[In]

Int[750*x - 750*x^2 + 350*x^6 - 150*x^2*Log[2],x]

[Out]

375*x^2 + 50*x^7 - 50*x^3*(5 + Log[2])

Rule 6

Int[(u_.)*((w_.) + (a_.)*(v_) + (b_.)*(v_))^(p_.), x_Symbol] :> Int[u*((a + b)*v + w)^p, x] /; FreeQ[{a, b}, x
] &&  !FreeQ[v, x]

Rubi steps

\begin {gather*} \begin {aligned} \text {integral} &=\int \left (750 x+350 x^6+x^2 (-750-150 \log (2))\right ) \, dx\\ &=375 x^2+50 x^7-50 x^3 (5+\log (2))\\ \end {aligned} \end {gather*}

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Mathematica [A]  time = 0.00, size = 23, normalized size = 0.96 \begin {gather*} 375 x^2-250 x^3+50 x^7-50 x^3 \log (2) \end {gather*}

Antiderivative was successfully verified.

[In]

Integrate[750*x - 750*x^2 + 350*x^6 - 150*x^2*Log[2],x]

[Out]

375*x^2 - 250*x^3 + 50*x^7 - 50*x^3*Log[2]

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fricas [A]  time = 0.64, size = 23, normalized size = 0.96 \begin {gather*} 50 \, x^{7} - 50 \, x^{3} \log \relax (2) - 250 \, x^{3} + 375 \, x^{2} \end {gather*}

Verification of antiderivative is not currently implemented for this CAS.

[In]

integrate(-150*x^2*log(2)+350*x^6-750*x^2+750*x,x, algorithm="fricas")

[Out]

50*x^7 - 50*x^3*log(2) - 250*x^3 + 375*x^2

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giac [A]  time = 0.34, size = 23, normalized size = 0.96 \begin {gather*} 50 \, x^{7} - 50 \, x^{3} \log \relax (2) - 250 \, x^{3} + 375 \, x^{2} \end {gather*}

Verification of antiderivative is not currently implemented for this CAS.

[In]

integrate(-150*x^2*log(2)+350*x^6-750*x^2+750*x,x, algorithm="giac")

[Out]

50*x^7 - 50*x^3*log(2) - 250*x^3 + 375*x^2

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maple [A]  time = 0.03, size = 21, normalized size = 0.88

method	result	size
gosper	\(-25 x^{2} \left (-2 x^{5}+2 x \ln \relax (2)+10 x -15\right )\)	\(21\)
norman	\(\left (-50 \ln \relax (2)-250\right ) x^{3}+375 x^{2}+50 x^{7}\)	\(22\)
default	\(-50 x^{3} \ln \relax (2)+50 x^{7}-250 x^{3}+375 x^{2}\)	\(24\)
risch	\(-50 x^{3} \ln \relax (2)+50 x^{7}-250 x^{3}+375 x^{2}\)	\(24\)

Verification of antiderivative is not currently implemented for this CAS.

[In]

int(-150*x^2*ln(2)+350*x^6-750*x^2+750*x,x,method=_RETURNVERBOSE)

[Out]

-25*x^2*(-2*x^5+2*x*ln(2)+10*x-15)

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maxima [A]  time = 0.47, size = 23, normalized size = 0.96 \begin {gather*} 50 \, x^{7} - 50 \, x^{3} \log \relax (2) - 250 \, x^{3} + 375 \, x^{2} \end {gather*}

Verification of antiderivative is not currently implemented for this CAS.

[In]

integrate(-150*x^2*log(2)+350*x^6-750*x^2+750*x,x, algorithm="maxima")

[Out]

50*x^7 - 50*x^3*log(2) - 250*x^3 + 375*x^2

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mupad [B]  time = 0.04, size = 22, normalized size = 0.92 \begin {gather*} 50\,x^7+\left (-50\,\ln \relax (2)-250\right )\,x^3+375\,x^2 \end {gather*}

Verification of antiderivative is not currently implemented for this CAS.

[In]

int(750*x - 150*x^2*log(2) - 750*x^2 + 350*x^6,x)

[Out]

375*x^2 - x^3*(50*log(2) + 250) + 50*x^7

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sympy [A]  time = 0.06, size = 20, normalized size = 0.83 \begin {gather*} 50 x^{7} + x^{3} \left (-250 - 50 \log {\relax (2 )}\right ) + 375 x^{2} \end {gather*}

Verification of antiderivative is not currently implemented for this CAS.

[In]

integrate(-150*x**2*ln(2)+350*x**6-750*x**2+750*x,x)

[Out]

50*x**7 + x**3*(-250 - 50*log(2)) + 375*x**2

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