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

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

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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 = {} $$\begin{array}{c}\int x^{-3+x^2}(-2+x^2+2x^2\log (x))dx\end{array}$$

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

$$\begin{array}{c}\begin{array}{rl}\text{integral}& =\int (-2x^{-3+x^2}+x^{-1+x^2}+2x^{-1+x^2}\log (x))dx\\ & =-(2\int x^{-3+x^2}dx)+2\int x^{-1+x^2}\log (x)dx+\int x^{-1+x^2}dx\\ & =-(2\int x^{-3+x^2}dx)-2\int \frac{\int x^{-1+x^2}dx}{x}dx+(2\log (x))\int x^{-1+x^2}dx+\int x^{-1+x^2}dx\end{array}\end{array}$$

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

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 $$\begin{array}{c}\frac{x^{\left(x^2\right)}}{x^2}\end{array}$$

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 $$\begin{array}{c}\frac{x^{\left(x^2\right)}}{x^2}\end{array}$$

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	$\frac{{\mathrm{e}}^{x^2\ln (x)}}{x^2}$	$12$

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 $$\begin{array}{c}\frac{x^{\left(x^2\right)}}{x^2}\end{array}$$

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 $$\begin{array}{c}{x}^{x^2-2}\end{array}$$

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 $$\begin{array}{c}\frac{e^{x^2\log (x)}}{x^2}\end{array}$$

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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