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

Optimal result

Integrand size = 7, antiderivative size = 15 \[ \int (-1+2 x \log (5)) \, dx=1-x+\left (-10+x^2+\log (2)\right ) \log (5) \]

[Out]

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

Rubi [A] (verified)

Time = 0.00 (sec) , antiderivative size = 10, normalized size of antiderivative = 0.67, number of steps used = 1, number of rules used = 0, \(\frac {\text {number of rules}}{\text {integrand size}}\) = 0.000, Rules used = {} \[ \int (-1+2 x \log (5)) \, dx=x^2 \log (5)-x \]

[In]

Int[-1 + 2*x*Log[5],x]

[Out]

-x + x^2*Log[5]

Rubi steps \begin{align*} \text {integral}& = -x+x^2 \log (5) \\ \end{align*}

Mathematica [A] (verified)

Time = 0.00 (sec) , antiderivative size = 10, normalized size of antiderivative = 0.67 \[ \int (-1+2 x \log (5)) \, dx=-x+x^2 \log (5) \]

[In]

Integrate[-1 + 2*x*Log[5],x]

[Out]

-x + x^2*Log[5]

Maple [A] (verified)

Time = 0.02 (sec) , antiderivative size = 11, normalized size of antiderivative = 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	\(x^{2} \ln \left (5\right )-x\)	\(11\)
parallelrisch	\(x^{2} \ln \left (5\right )-x\)	\(11\)
parts	\(x^{2} \ln \left (5\right )-x\)	\(11\)

[In]

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

[Out]

x^2*ln(5)-x

Fricas [A] (verification not implemented)

none

Time = 0.24 (sec) , antiderivative size = 10, normalized size of antiderivative = 0.67 \[ \int (-1+2 x \log (5)) \, dx=x^{2} \log \left (5\right ) - x \]

[In]

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

[Out]

x^2*log(5) - x

Sympy [A] (verification not implemented)

Time = 0.02 (sec) , antiderivative size = 7, normalized size of antiderivative = 0.47 \[ \int (-1+2 x \log (5)) \, dx=x^{2} \log {\left (5 \right )} - x \]

[In]

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

[Out]

x**2*log(5) - x

Maxima [A] (verification not implemented)

none

Time = 0.19 (sec) , antiderivative size = 10, normalized size of antiderivative = 0.67 \[ \int (-1+2 x \log (5)) \, dx=x^{2} \log \left (5\right ) - x \]

[In]

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

[Out]

x^2*log(5) - x

Giac [A] (verification not implemented)

none

Time = 0.27 (sec) , antiderivative size = 10, normalized size of antiderivative = 0.67 \[ \int (-1+2 x \log (5)) \, dx=x^{2} \log \left (5\right ) - x \]

[In]

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

[Out]

x^2*log(5) - x

Mupad [B] (verification not implemented)

Time = 0.03 (sec) , antiderivative size = 10, normalized size of antiderivative = 0.67 \[ \int (-1+2 x \log (5)) \, dx=x^2\,\ln \left (5\right )-x \]

[In]

int(2*x*log(5) - 1,x)

[Out]

x^2*log(5) - x