3.52.60 \(\int x^{-11+2 x} (-10+2 x+2 x \log (x)) \, dx\)

Optimal. Leaf size=21 \[ i \pi +x^{2 (-5+x)}+\log \left (-\frac {5}{2}+e^6\right ) \]

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Rubi [F]  time = 0.12, antiderivative size = 0, normalized size of antiderivative = 0.00, number of steps used = 0, number of rules used = 0, integrand size = 0, \(\frac {\text {number of rules}}{\text {integrand size}}\) = 0.000, Rules used = {} \begin {gather*} \int x^{-11+2 x} (-10+2 x+2 x \log (x)) \, dx \end {gather*}

Verification is not applicable to the result.

[In]

Int[x^(-11 + 2*x)*(-10 + 2*x + 2*x*Log[x]),x]

[Out]

-10*Defer[Int][x^(-11 + 2*x), x] + 2*Defer[Int][x^(-10 + 2*x), x] + 2*Log[x]*Defer[Int][x^(-10 + 2*x), x] - 2*
Defer[Int][Defer[Int][x^(-10 + 2*x), x]/x, x]

Rubi steps

\begin {gather*} \begin {aligned} \text {integral} &=\int 2 x^{-11+2 x} (-5+x+x \log (x)) \, dx\\ &=2 \int x^{-11+2 x} (-5+x+x \log (x)) \, dx\\ &=2 \int \left (-5 x^{-11+2 x}+x^{-10+2 x}+x^{-10+2 x} \log (x)\right ) \, dx\\ &=2 \int x^{-10+2 x} \, dx+2 \int x^{-10+2 x} \log (x) \, dx-10 \int x^{-11+2 x} \, dx\\ &=2 \int x^{-10+2 x} \, dx-2 \int \frac {\int x^{-10+2 x} \, dx}{x} \, dx-10 \int x^{-11+2 x} \, dx+(2 \log (x)) \int x^{-10+2 x} \, dx\\ \end {aligned} \end {gather*}

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Mathematica [A]  time = 0.03, size = 7, normalized size = 0.33 \begin {gather*} x^{-10+2 x} \end {gather*}

Antiderivative was successfully verified.

[In]

Integrate[x^(-11 + 2*x)*(-10 + 2*x + 2*x*Log[x]),x]

[Out]

x^(-10 + 2*x)

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fricas [A]  time = 0.57, size = 7, normalized size = 0.33 \begin {gather*} x^{2 \, x - 10} \end {gather*}

Verification of antiderivative is not currently implemented for this CAS.

[In]

integrate((2*x*log(x)+2*x-10)*exp((2*x-10)*log(x))/x,x, algorithm="fricas")

[Out]

x^(2*x - 10)

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giac [A]  time = 0.16, size = 7, normalized size = 0.33 \begin {gather*} x^{2 \, x - 10} \end {gather*}

Verification of antiderivative is not currently implemented for this CAS.

[In]

integrate((2*x*log(x)+2*x-10)*exp((2*x-10)*log(x))/x,x, algorithm="giac")

[Out]

x^(2*x - 10)

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maple [A]  time = 0.02, size = 8, normalized size = 0.38

method	result	size
risch	\(x^{2 x -10}\)	\(8\)
norman	\({\mathrm e}^{\left (2 x -10\right ) \ln \relax (x )}\)	\(10\)

Verification of antiderivative is not currently implemented for this CAS.

[In]

int((2*x*ln(x)+2*x-10)*exp((2*x-10)*ln(x))/x,x,method=_RETURNVERBOSE)

[Out]

x^(2*x-10)

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maxima [A]  time = 0.40, size = 9, normalized size = 0.43 \begin {gather*} \frac {x^{2 \, x}}{x^{10}} \end {gather*}

Verification of antiderivative is not currently implemented for this CAS.

[In]

integrate((2*x*log(x)+2*x-10)*exp((2*x-10)*log(x))/x,x, algorithm="maxima")

[Out]

x^(2*x)/x^10

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mupad [B]  time = 3.34, size = 7, normalized size = 0.33 \begin {gather*} x^{2\,x-10} \end {gather*}

Verification of antiderivative is not currently implemented for this CAS.

[In]

int((exp(log(x)*(2*x - 10))*(2*x + 2*x*log(x) - 10))/x,x)

[Out]

x^(2*x - 10)

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sympy [A]  time = 0.26, size = 8, normalized size = 0.38 \begin {gather*} e^{\left (2 x - 10\right ) \log {\relax (x )}} \end {gather*}

Verification of antiderivative is not currently implemented for this CAS.

[In]

integrate((2*x*ln(x)+2*x-10)*exp((2*x-10)*ln(x))/x,x)

[Out]

exp((2*x - 10)*log(x))

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