3.38.48 \(\int (-470+50 x+10 \log (16)) \, dx\)

Optimal. Leaf size=14 \[ (-5+2 (-21+x)+3 x+\log (16))^2 \]

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Rubi [A]  time = 0.01, antiderivative size = 15, normalized size of antiderivative = 1.07, number of steps used = 1, number of rules used = 0, integrand size = 9, \(\frac {\text {number of rules}}{\text {integrand size}}\) = 0.000, Rules used = {} \begin {gather*} 25 x^2-10 x (47-\log (16)) \end {gather*}

Antiderivative was successfully verified.

[In]

Int[-470 + 50*x + 10*Log[16],x]

[Out]

25*x^2 - 10*x*(47 - Log[16])

Rubi steps

\begin {gather*} \begin {aligned} \text {integral} &=25 x^2-10 x (47-\log (16))\\ \end {aligned} \end {gather*}

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Mathematica [A]  time = 0.00, size = 14, normalized size = 1.00 \begin {gather*} -470 x+25 x^2+10 x \log (16) \end {gather*}

Antiderivative was successfully verified.

[In]

Integrate[-470 + 50*x + 10*Log[16],x]

[Out]

-470*x + 25*x^2 + 10*x*Log[16]

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fricas [A]  time = 0.65, size = 14, normalized size = 1.00 \begin {gather*} 25 \, x^{2} + 40 \, x \log \relax (2) - 470 \, x \end {gather*}

Verification of antiderivative is not currently implemented for this CAS.

[In]

integrate(40*log(2)+50*x-470,x, algorithm="fricas")

[Out]

25*x^2 + 40*x*log(2) - 470*x

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giac [A]  time = 0.14, size = 14, normalized size = 1.00 \begin {gather*} 25 \, x^{2} + 40 \, x \log \relax (2) - 470 \, x \end {gather*}

Verification of antiderivative is not currently implemented for this CAS.

[In]

integrate(40*log(2)+50*x-470,x, algorithm="giac")

[Out]

25*x^2 + 40*x*log(2) - 470*x

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maple [A]  time = 0.02, size = 13, normalized size = 0.93

method	result	size
gosper	\(5 x \left (5 x +8 \ln \relax (2)-94\right )\)	\(13\)
default	\(40 x \ln \relax (2)+25 x^{2}-470 x\)	\(15\)
norman	\(\left (40 \ln \relax (2)-470\right ) x +25 x^{2}\)	\(15\)
risch	\(40 x \ln \relax (2)+25 x^{2}-470 x\)	\(15\)

Verification of antiderivative is not currently implemented for this CAS.

[In]

int(40*ln(2)+50*x-470,x,method=_RETURNVERBOSE)

[Out]

5*x*(5*x+8*ln(2)-94)

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maxima [A]  time = 0.42, size = 14, normalized size = 1.00 \begin {gather*} 25 \, x^{2} + 40 \, x \log \relax (2) - 470 \, x \end {gather*}

Verification of antiderivative is not currently implemented for this CAS.

[In]

integrate(40*log(2)+50*x-470,x, algorithm="maxima")

[Out]

25*x^2 + 40*x*log(2) - 470*x

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mupad [B]  time = 2.11, size = 14, normalized size = 1.00 \begin {gather*} 25\,x^2+\left (40\,\ln \relax (2)-470\right )\,x \end {gather*}

Verification of antiderivative is not currently implemented for this CAS.

[In]

int(50*x + 40*log(2) - 470,x)

[Out]

x*(40*log(2) - 470) + 25*x^2

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sympy [A]  time = 0.05, size = 12, normalized size = 0.86 \begin {gather*} 25 x^{2} + x \left (-470 + 40 \log {\relax (2 )}\right ) \end {gather*}

Verification of antiderivative is not currently implemented for this CAS.

[In]

integrate(40*ln(2)+50*x-470,x)

[Out]

25*x**2 + x*(-470 + 40*log(2))

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