3.41.74 \(\int x^{-3+x^2} (-2+x^2+2 x^2 \log (x)) \, dx\)

Optimal. Leaf size=15 \[ \frac {225 x^2+x^{x^2}}{x^2} \]

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Rubi [F]  time = 0.09, 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^{-3+x^2} \left (-2+x^2+2 x^2 \log (x)\right ) \, dx \end {gather*}

Verification is not applicable to the result.

[In]

Int[x^(-3 + x^2)*(-2 + x^2 + 2*x^2*Log[x]),x]

[Out]

-2*Defer[Int][x^(-3 + x^2), x] + Defer[Int][x^(-1 + x^2), x] + 2*Log[x]*Defer[Int][x^(-1 + x^2), x] - 2*Defer[
Int][Defer[Int][x^(-1 + x^2), x]/x, x]

Rubi steps

\begin {gather*} \begin {aligned} \text {integral} &=\int \left (-2 x^{-3+x^2}+x^{-1+x^2}+2 x^{-1+x^2} \log (x)\right ) \, dx\\ &=-\left (2 \int x^{-3+x^2} \, dx\right )+2 \int x^{-1+x^2} \log (x) \, dx+\int x^{-1+x^2} \, dx\\ &=-\left (2 \int x^{-3+x^2} \, dx\right )-2 \int \frac {\int x^{-1+x^2} \, dx}{x} \, dx+(2 \log (x)) \int x^{-1+x^2} \, dx+\int x^{-1+x^2} \, dx\\ \end {aligned} \end {gather*}

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Mathematica [A]  time = 0.04, size = 7, normalized size = 0.47 \begin {gather*} x^{-2+x^2} \end {gather*}

Antiderivative was successfully verified.

[In]

Integrate[x^(-3 + x^2)*(-2 + x^2 + 2*x^2*Log[x]),x]

[Out]

x^(-2 + x^2)

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fricas [A]  time = 0.76, size = 9, normalized size = 0.60 \begin {gather*} \frac {x^{\left (x^{2}\right )}}{x^{2}} \end {gather*}

Verification of antiderivative is not currently implemented for this CAS.

[In]

integrate((2*x^2*log(x)+x^2-2)*exp(x^2*log(x))/x^3,x, algorithm="fricas")

[Out]

x^(x^2)/x^2

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giac [A]  time = 0.18, size = 9, normalized size = 0.60 \begin {gather*} \frac {x^{\left (x^{2}\right )}}{x^{2}} \end {gather*}

Verification of antiderivative is not currently implemented for this CAS.

[In]

integrate((2*x^2*log(x)+x^2-2)*exp(x^2*log(x))/x^3,x, algorithm="giac")

[Out]

x^(x^2)/x^2

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maple [A]  time = 0.03, size = 10, normalized size = 0.67

method	result	size
risch	\(\frac {x^{x^{2}}}{x^{2}}\)	\(10\)
norman	\(\frac {{\mathrm e}^{x^{2} \ln \relax (x )}}{x^{2}}\)	\(12\)

Verification of antiderivative is not currently implemented for this CAS.

[In]

int((2*x^2*ln(x)+x^2-2)*exp(x^2*ln(x))/x^3,x,method=_RETURNVERBOSE)

[Out]

x^(x^2)/x^2

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maxima [A]  time = 0.41, size = 9, normalized size = 0.60 \begin {gather*} \frac {x^{\left (x^{2}\right )}}{x^{2}} \end {gather*}

Verification of antiderivative is not currently implemented for this CAS.

[In]

integrate((2*x^2*log(x)+x^2-2)*exp(x^2*log(x))/x^3,x, algorithm="maxima")

[Out]

x^(x^2)/x^2

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mupad [B]  time = 3.13, size = 7, normalized size = 0.47 \begin {gather*} x^{x^2-2} \end {gather*}

Verification of antiderivative is not currently implemented for this CAS.

[In]

int((exp(x^2*log(x))*(2*x^2*log(x) + x^2 - 2))/x^3,x)

[Out]

x^(x^2 - 2)

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sympy [A]  time = 0.24, size = 10, normalized size = 0.67 \begin {gather*} \frac {e^{x^{2} \log {\relax (x )}}}{x^{2}} \end {gather*}

Verification of antiderivative is not currently implemented for this CAS.

[In]

integrate((2*x**2*ln(x)+x**2-2)*exp(x**2*ln(x))/x**3,x)

[Out]

exp(x**2*log(x))/x**2

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