3.74.57 \(\int (-1+2 x \log (5)) \, dx\) [7357]

Optimal. Leaf size=15 \[ 1-x+\left (-10+x^2+\log (2)\right ) \log (5) \]

[Out]

1-x+ln(5)*(x^2-10+ln(2))

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Rubi [A]
time = 0.00, antiderivative size = 10, normalized size of antiderivative = 0.67, number of steps used = 1, number of rules used = 0, integrand size = 7, \(\frac {\text {number of rules}}{\text {integrand size}}\) = 0.000, Rules used = {} \begin {gather*} x^2 \log (5)-x \end {gather*}

Antiderivative was successfully verified.

[In]

Int[-1 + 2*x*Log[5],x]

[Out]

-x + x^2*Log[5]

Rubi steps

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

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Mathematica [A]
time = 0.00, size = 10, normalized size = 0.67 \begin {gather*} -x+x^2 \log (5) \end {gather*}

Antiderivative was successfully verified.

[In]

Integrate[-1 + 2*x*Log[5],x]

[Out]

-x + x^2*Log[5]

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Maple [A]
time = 0.36, size = 11, normalized size = 0.73

method	result	size
gosper	\(x^{2} \ln \left (5\right )-x\)	\(11\)
default	\(x^{2} \ln \left (5\right )-x\)	\(11\)
norman	\(x^{2} \ln \left (5\right )-x\)	\(11\)
risch	\(x^{2} \ln \left (5\right )-x\)	\(11\)

Verification of antiderivative is not currently implemented for this CAS.

[In]

int(2*x*ln(5)-1,x,method=_RETURNVERBOSE)

[Out]

x^2*ln(5)-x

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Maxima [A]
time = 0.27, size = 10, normalized size = 0.67 \begin {gather*} x^{2} \log \left (5\right ) - x \end {gather*}

Verification of antiderivative is not currently implemented for this CAS.

[In]

integrate(2*x*log(5)-1,x, algorithm="maxima")

[Out]

x^2*log(5) - x

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Fricas [A]
time = 0.41, size = 10, normalized size = 0.67 \begin {gather*} x^{2} \log \left (5\right ) - x \end {gather*}

Verification of antiderivative is not currently implemented for this CAS.

[In]

integrate(2*x*log(5)-1,x, algorithm="fricas")

[Out]

x^2*log(5) - x

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Sympy [A]
time = 0.01, size = 7, normalized size = 0.47 \begin {gather*} x^{2} \log {\left (5 \right )} - x \end {gather*}

Verification of antiderivative is not currently implemented for this CAS.

[In]

integrate(2*x*ln(5)-1,x)

[Out]

x**2*log(5) - x

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Giac [A]
time = 0.40, size = 10, normalized size = 0.67 \begin {gather*} x^{2} \log \left (5\right ) - x \end {gather*}

Verification of antiderivative is not currently implemented for this CAS.

[In]

integrate(2*x*log(5)-1,x, algorithm="giac")

[Out]

x^2*log(5) - x

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Mupad [B]
time = 0.04, size = 10, normalized size = 0.67 \begin {gather*} x^2\,\ln \left (5\right )-x \end {gather*}

Verification of antiderivative is not currently implemented for this CAS.

[In]

int(2*x*log(5) - 1,x)

[Out]

x^2*log(5) - x

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