3.99.52 \(\int \frac {e^{x^2} (-60 x^3+2 x^4)-2 x^3 \log (-30+x)+(30 x^2-x^3+e^{x^2} (120 x^3-4 x^4)) \log ^2(-30+x)+(30 x-31 x^2+x^3+e^{x^2} (-60 x^3+2 x^4)) \log ^4(-30+x)+(e^{x^2} (120 x^2-4 x^3) \log ^2(-30+x)+(-60 x+2 x^2+e^{x^2} (-120 x^2+4 x^3)) \log ^4(-30+x)) \log (x)+e^{x^2} (-60 x+2 x^2) \log ^4(-30+x) \log ^2(x)}{-30 x^2+x^3+(60 x^2-2 x^3) \log ^2(-30+x)+(-30 x^2+x^3) \log ^4(-30+x)+((60 x-2 x^2) \log ^2(-30+x)+(-60 x+2 x^2) \log ^4(-30+x)) \log (x)+(-30+x) \log ^4(-30+x) \log ^2(x)} \, dx\)

Optimal. Leaf size=29 \[ e^{x^2}-\frac {x^2}{-x+\frac {x}{\log ^2(-30+x)}-\log (x)} \]

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Rubi [F]  time = 7.12, 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 \frac {e^{x^2} \left (-60 x^3+2 x^4\right )-2 x^3 \log (-30+x)+\left (30 x^2-x^3+e^{x^2} \left (120 x^3-4 x^4\right )\right ) \log ^2(-30+x)+\left (30 x-31 x^2+x^3+e^{x^2} \left (-60 x^3+2 x^4\right )\right ) \log ^4(-30+x)+\left (e^{x^2} \left (120 x^2-4 x^3\right ) \log ^2(-30+x)+\left (-60 x+2 x^2+e^{x^2} \left (-120 x^2+4 x^3\right )\right ) \log ^4(-30+x)\right ) \log (x)+e^{x^2} \left (-60 x+2 x^2\right ) \log ^4(-30+x) \log ^2(x)}{-30 x^2+x^3+\left (60 x^2-2 x^3\right ) \log ^2(-30+x)+\left (-30 x^2+x^3\right ) \log ^4(-30+x)+\left (\left (60 x-2 x^2\right ) \log ^2(-30+x)+\left (-60 x+2 x^2\right ) \log ^4(-30+x)\right ) \log (x)+(-30+x) \log ^4(-30+x) \log ^2(x)} \, dx \end {gather*}

Verification is not applicable to the result.

[In]

Int[(E^x^2*(-60*x^3 + 2*x^4) - 2*x^3*Log[-30 + x] + (30*x^2 - x^3 + E^x^2*(120*x^3 - 4*x^4))*Log[-30 + x]^2 +
(30*x - 31*x^2 + x^3 + E^x^2*(-60*x^3 + 2*x^4))*Log[-30 + x]^4 + (E^x^2*(120*x^2 - 4*x^3)*Log[-30 + x]^2 + (-6
0*x + 2*x^2 + E^x^2*(-120*x^2 + 4*x^3))*Log[-30 + x]^4)*Log[x] + E^x^2*(-60*x + 2*x^2)*Log[-30 + x]^4*Log[x]^2
)/(-30*x^2 + x^3 + (60*x^2 - 2*x^3)*Log[-30 + x]^2 + (-30*x^2 + x^3)*Log[-30 + x]^4 + ((60*x - 2*x^2)*Log[-30
+ x]^2 + (-60*x + 2*x^2)*Log[-30 + x]^4)*Log[x] + (-30 + x)*Log[-30 + x]^4*Log[x]^2),x]

[Out]

E^x^2 - 1800*Defer[Int][Log[-30 + x]/(x - Log[-30 + x]^2*(x + Log[x]))^2, x] - 54000*Defer[Int][Log[-30 + x]/(
(-30 + x)*(x - Log[-30 + x]^2*(x + Log[x]))^2), x] - 60*Defer[Int][(x*Log[-30 + x])/(x - Log[-30 + x]^2*(x + L
og[x]))^2, x] - 2*Defer[Int][(x^2*Log[-30 + x])/(x - Log[-30 + x]^2*(x + Log[x]))^2, x] + Defer[Int][(x^2*Log[
-30 + x]^2)/(x - Log[-30 + x]^2*(x + Log[x]))^2, x] - Defer[Int][(x*Log[-30 + x]^4)/(x - Log[-30 + x]^2*(x + L
og[x]))^2, x] - Defer[Int][(x^2*Log[-30 + x]^4)/(x - Log[-30 + x]^2*(x + Log[x]))^2, x] + 2*Defer[Int][(x*Log[
-30 + x]^2)/(-x + Log[-30 + x]^2*(x + Log[x])), x]

Rubi steps

\begin {gather*} \begin {aligned} \text {integral} &=\int \frac {x \left (-2 e^{x^2} (-30+x) x^2+2 x^2 \log (-30+x)+(-30+x) x \log ^2(-30+x) \left (1+4 e^{x^2} x+4 e^{x^2} \log (x)\right )-(-30+x) \log ^4(-30+x) \left (-1+x+2 e^{x^2} x^2+\left (2+4 e^{x^2} x\right ) \log (x)+2 e^{x^2} \log ^2(x)\right )\right )}{(30-x) \left (x-\log ^2(-30+x) (x+\log (x))\right )^2} \, dx\\ &=\int \left (2 e^{x^2} x-\frac {2 x^3 \log (-30+x)}{(-30+x) \left (-x+x \log ^2(-30+x)+\log ^2(-30+x) \log (x)\right )^2}-\frac {x^2 \log ^2(-30+x)}{\left (-x+x \log ^2(-30+x)+\log ^2(-30+x) \log (x)\right )^2}-\frac {x \log ^4(-30+x)}{\left (-x+x \log ^2(-30+x)+\log ^2(-30+x) \log (x)\right )^2}+\frac {x^2 \log ^4(-30+x)}{\left (-x+x \log ^2(-30+x)+\log ^2(-30+x) \log (x)\right )^2}+\frac {2 x \log ^4(-30+x) \log (x)}{\left (-x+x \log ^2(-30+x)+\log ^2(-30+x) \log (x)\right )^2}\right ) \, dx\\ &=2 \int e^{x^2} x \, dx-2 \int \frac {x^3 \log (-30+x)}{(-30+x) \left (-x+x \log ^2(-30+x)+\log ^2(-30+x) \log (x)\right )^2} \, dx+2 \int \frac {x \log ^4(-30+x) \log (x)}{\left (-x+x \log ^2(-30+x)+\log ^2(-30+x) \log (x)\right )^2} \, dx-\int \frac {x^2 \log ^2(-30+x)}{\left (-x+x \log ^2(-30+x)+\log ^2(-30+x) \log (x)\right )^2} \, dx-\int \frac {x \log ^4(-30+x)}{\left (-x+x \log ^2(-30+x)+\log ^2(-30+x) \log (x)\right )^2} \, dx+\int \frac {x^2 \log ^4(-30+x)}{\left (-x+x \log ^2(-30+x)+\log ^2(-30+x) \log (x)\right )^2} \, dx\\ &=e^{x^2}-2 \int \frac {x^3 \log (-30+x)}{(-30+x) \left (x-\log ^2(-30+x) (x+\log (x))\right )^2} \, dx+2 \int \frac {x \log ^4(-30+x) \log (x)}{\left (x-\log ^2(-30+x) (x+\log (x))\right )^2} \, dx-\int \frac {x^2 \log ^2(-30+x)}{\left (x-\log ^2(-30+x) (x+\log (x))\right )^2} \, dx-\int \frac {x \log ^4(-30+x)}{\left (x-\log ^2(-30+x) (x+\log (x))\right )^2} \, dx+\int \frac {x^2 \log ^4(-30+x)}{\left (x-\log ^2(-30+x) (x+\log (x))\right )^2} \, dx\\ &=e^{x^2}-2 \int \left (\frac {900 \log (-30+x)}{\left (-x+x \log ^2(-30+x)+\log ^2(-30+x) \log (x)\right )^2}+\frac {27000 \log (-30+x)}{(-30+x) \left (-x+x \log ^2(-30+x)+\log ^2(-30+x) \log (x)\right )^2}+\frac {30 x \log (-30+x)}{\left (-x+x \log ^2(-30+x)+\log ^2(-30+x) \log (x)\right )^2}+\frac {x^2 \log (-30+x)}{\left (-x+x \log ^2(-30+x)+\log ^2(-30+x) \log (x)\right )^2}\right ) \, dx+2 \int \left (-\frac {x^2 \log ^2(-30+x) \left (-1+\log ^2(-30+x)\right )}{\left (-x+x \log ^2(-30+x)+\log ^2(-30+x) \log (x)\right )^2}+\frac {x \log ^2(-30+x)}{-x+x \log ^2(-30+x)+\log ^2(-30+x) \log (x)}\right ) \, dx-\int \frac {x^2 \log ^2(-30+x)}{\left (x-\log ^2(-30+x) (x+\log (x))\right )^2} \, dx-\int \frac {x \log ^4(-30+x)}{\left (x-\log ^2(-30+x) (x+\log (x))\right )^2} \, dx+\int \frac {x^2 \log ^4(-30+x)}{\left (x-\log ^2(-30+x) (x+\log (x))\right )^2} \, dx\\ &=e^{x^2}-2 \int \frac {x^2 \log (-30+x)}{\left (-x+x \log ^2(-30+x)+\log ^2(-30+x) \log (x)\right )^2} \, dx-2 \int \frac {x^2 \log ^2(-30+x) \left (-1+\log ^2(-30+x)\right )}{\left (-x+x \log ^2(-30+x)+\log ^2(-30+x) \log (x)\right )^2} \, dx+2 \int \frac {x \log ^2(-30+x)}{-x+x \log ^2(-30+x)+\log ^2(-30+x) \log (x)} \, dx-60 \int \frac {x \log (-30+x)}{\left (-x+x \log ^2(-30+x)+\log ^2(-30+x) \log (x)\right )^2} \, dx-1800 \int \frac {\log (-30+x)}{\left (-x+x \log ^2(-30+x)+\log ^2(-30+x) \log (x)\right )^2} \, dx-54000 \int \frac {\log (-30+x)}{(-30+x) \left (-x+x \log ^2(-30+x)+\log ^2(-30+x) \log (x)\right )^2} \, dx-\int \frac {x^2 \log ^2(-30+x)}{\left (x-\log ^2(-30+x) (x+\log (x))\right )^2} \, dx-\int \frac {x \log ^4(-30+x)}{\left (x-\log ^2(-30+x) (x+\log (x))\right )^2} \, dx+\int \frac {x^2 \log ^4(-30+x)}{\left (x-\log ^2(-30+x) (x+\log (x))\right )^2} \, dx\\ &=e^{x^2}-2 \int \frac {x^2 \log (-30+x)}{\left (x-\log ^2(-30+x) (x+\log (x))\right )^2} \, dx-2 \int \frac {x^2 \log ^2(-30+x) \left (-1+\log ^2(-30+x)\right )}{\left (x-\log ^2(-30+x) (x+\log (x))\right )^2} \, dx+2 \int \frac {x \log ^2(-30+x)}{-x+\log ^2(-30+x) (x+\log (x))} \, dx-60 \int \frac {x \log (-30+x)}{\left (x-\log ^2(-30+x) (x+\log (x))\right )^2} \, dx-1800 \int \frac {\log (-30+x)}{\left (x-\log ^2(-30+x) (x+\log (x))\right )^2} \, dx-54000 \int \frac {\log (-30+x)}{(-30+x) \left (x-\log ^2(-30+x) (x+\log (x))\right )^2} \, dx-\int \frac {x^2 \log ^2(-30+x)}{\left (x-\log ^2(-30+x) (x+\log (x))\right )^2} \, dx-\int \frac {x \log ^4(-30+x)}{\left (x-\log ^2(-30+x) (x+\log (x))\right )^2} \, dx+\int \frac {x^2 \log ^4(-30+x)}{\left (x-\log ^2(-30+x) (x+\log (x))\right )^2} \, dx\\ &=e^{x^2}-2 \int \frac {x^2 \log (-30+x)}{\left (x-\log ^2(-30+x) (x+\log (x))\right )^2} \, dx+2 \int \frac {x \log ^2(-30+x)}{-x+\log ^2(-30+x) (x+\log (x))} \, dx-2 \int \left (-\frac {x^2 \log ^2(-30+x)}{\left (-x+x \log ^2(-30+x)+\log ^2(-30+x) \log (x)\right )^2}+\frac {x^2 \log ^4(-30+x)}{\left (-x+x \log ^2(-30+x)+\log ^2(-30+x) \log (x)\right )^2}\right ) \, dx-60 \int \frac {x \log (-30+x)}{\left (x-\log ^2(-30+x) (x+\log (x))\right )^2} \, dx-1800 \int \frac {\log (-30+x)}{\left (x-\log ^2(-30+x) (x+\log (x))\right )^2} \, dx-54000 \int \frac {\log (-30+x)}{(-30+x) \left (x-\log ^2(-30+x) (x+\log (x))\right )^2} \, dx-\int \frac {x^2 \log ^2(-30+x)}{\left (x-\log ^2(-30+x) (x+\log (x))\right )^2} \, dx-\int \frac {x \log ^4(-30+x)}{\left (x-\log ^2(-30+x) (x+\log (x))\right )^2} \, dx+\int \frac {x^2 \log ^4(-30+x)}{\left (x-\log ^2(-30+x) (x+\log (x))\right )^2} \, dx\\ &=e^{x^2}+2 \int \frac {x^2 \log ^2(-30+x)}{\left (-x+x \log ^2(-30+x)+\log ^2(-30+x) \log (x)\right )^2} \, dx-2 \int \frac {x^2 \log ^4(-30+x)}{\left (-x+x \log ^2(-30+x)+\log ^2(-30+x) \log (x)\right )^2} \, dx-2 \int \frac {x^2 \log (-30+x)}{\left (x-\log ^2(-30+x) (x+\log (x))\right )^2} \, dx+2 \int \frac {x \log ^2(-30+x)}{-x+\log ^2(-30+x) (x+\log (x))} \, dx-60 \int \frac {x \log (-30+x)}{\left (x-\log ^2(-30+x) (x+\log (x))\right )^2} \, dx-1800 \int \frac {\log (-30+x)}{\left (x-\log ^2(-30+x) (x+\log (x))\right )^2} \, dx-54000 \int \frac {\log (-30+x)}{(-30+x) \left (x-\log ^2(-30+x) (x+\log (x))\right )^2} \, dx-\int \frac {x^2 \log ^2(-30+x)}{\left (x-\log ^2(-30+x) (x+\log (x))\right )^2} \, dx-\int \frac {x \log ^4(-30+x)}{\left (x-\log ^2(-30+x) (x+\log (x))\right )^2} \, dx+\int \frac {x^2 \log ^4(-30+x)}{\left (x-\log ^2(-30+x) (x+\log (x))\right )^2} \, dx\\ &=e^{x^2}-2 \int \frac {x^2 \log (-30+x)}{\left (x-\log ^2(-30+x) (x+\log (x))\right )^2} \, dx+2 \int \frac {x^2 \log ^2(-30+x)}{\left (x-\log ^2(-30+x) (x+\log (x))\right )^2} \, dx-2 \int \frac {x^2 \log ^4(-30+x)}{\left (x-\log ^2(-30+x) (x+\log (x))\right )^2} \, dx+2 \int \frac {x \log ^2(-30+x)}{-x+\log ^2(-30+x) (x+\log (x))} \, dx-60 \int \frac {x \log (-30+x)}{\left (x-\log ^2(-30+x) (x+\log (x))\right )^2} \, dx-1800 \int \frac {\log (-30+x)}{\left (x-\log ^2(-30+x) (x+\log (x))\right )^2} \, dx-54000 \int \frac {\log (-30+x)}{(-30+x) \left (x-\log ^2(-30+x) (x+\log (x))\right )^2} \, dx-\int \frac {x^2 \log ^2(-30+x)}{\left (x-\log ^2(-30+x) (x+\log (x))\right )^2} \, dx-\int \frac {x \log ^4(-30+x)}{\left (x-\log ^2(-30+x) (x+\log (x))\right )^2} \, dx+\int \frac {x^2 \log ^4(-30+x)}{\left (x-\log ^2(-30+x) (x+\log (x))\right )^2} \, dx\\ \end {aligned} \end {gather*}

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Mathematica [A]  time = 0.21, size = 33, normalized size = 1.14 \begin {gather*} e^{x^2}+\frac {x^2 \log ^2(-30+x)}{-x+\log ^2(-30+x) (x+\log (x))} \end {gather*}

Antiderivative was successfully verified.

[In]

Integrate[(E^x^2*(-60*x^3 + 2*x^4) - 2*x^3*Log[-30 + x] + (30*x^2 - x^3 + E^x^2*(120*x^3 - 4*x^4))*Log[-30 + x
]^2 + (30*x - 31*x^2 + x^3 + E^x^2*(-60*x^3 + 2*x^4))*Log[-30 + x]^4 + (E^x^2*(120*x^2 - 4*x^3)*Log[-30 + x]^2
+ (-60*x + 2*x^2 + E^x^2*(-120*x^2 + 4*x^3))*Log[-30 + x]^4)*Log[x] + E^x^2*(-60*x + 2*x^2)*Log[-30 + x]^4*Lo
g[x]^2)/(-30*x^2 + x^3 + (60*x^2 - 2*x^3)*Log[-30 + x]^2 + (-30*x^2 + x^3)*Log[-30 + x]^4 + ((60*x - 2*x^2)*Lo
g[-30 + x]^2 + (-60*x + 2*x^2)*Log[-30 + x]^4)*Log[x] + (-30 + x)*Log[-30 + x]^4*Log[x]^2),x]

[Out]

E^x^2 + (x^2*Log[-30 + x]^2)/(-x + Log[-30 + x]^2*(x + Log[x]))

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fricas [B]  time = 1.07, size = 62, normalized size = 2.14 \begin {gather*} \frac {e^{\left (x^{2}\right )} \log \left (x - 30\right )^{2} \log \relax (x) + {\left (x^{2} + x e^{\left (x^{2}\right )}\right )} \log \left (x - 30\right )^{2} - x e^{\left (x^{2}\right )}}{x \log \left (x - 30\right )^{2} + \log \left (x - 30\right )^{2} \log \relax (x) - x} \end {gather*}

Verification of antiderivative is not currently implemented for this CAS.

[In]

integrate(((2*x^2-60*x)*exp(x^2)*log(x-30)^4*log(x)^2+(((4*x^3-120*x^2)*exp(x^2)+2*x^2-60*x)*log(x-30)^4+(-4*x
^3+120*x^2)*exp(x^2)*log(x-30)^2)*log(x)+((2*x^4-60*x^3)*exp(x^2)+x^3-31*x^2+30*x)*log(x-30)^4+((-4*x^4+120*x^
3)*exp(x^2)-x^3+30*x^2)*log(x-30)^2-2*x^3*log(x-30)+(2*x^4-60*x^3)*exp(x^2))/((x-30)*log(x-30)^4*log(x)^2+((2*
x^2-60*x)*log(x-30)^4+(-2*x^2+60*x)*log(x-30)^2)*log(x)+(x^3-30*x^2)*log(x-30)^4+(-2*x^3+60*x^2)*log(x-30)^2+x
^3-30*x^2),x, algorithm="fricas")

[Out]

(e^(x^2)*log(x - 30)^2*log(x) + (x^2 + x*e^(x^2))*log(x - 30)^2 - x*e^(x^2))/(x*log(x - 30)^2 + log(x - 30)^2*
log(x) - x)

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giac [B]  time = 0.87, size = 67, normalized size = 2.31 \begin {gather*} \frac {x^{2} \log \left (x - 30\right )^{2} + x e^{\left (x^{2}\right )} \log \left (x - 30\right )^{2} + e^{\left (x^{2}\right )} \log \left (x - 30\right )^{2} \log \relax (x) - x e^{\left (x^{2}\right )}}{x \log \left (x - 30\right )^{2} + \log \left (x - 30\right )^{2} \log \relax (x) - x} \end {gather*}

Verification of antiderivative is not currently implemented for this CAS.

[In]

integrate(((2*x^2-60*x)*exp(x^2)*log(x-30)^4*log(x)^2+(((4*x^3-120*x^2)*exp(x^2)+2*x^2-60*x)*log(x-30)^4+(-4*x
^3+120*x^2)*exp(x^2)*log(x-30)^2)*log(x)+((2*x^4-60*x^3)*exp(x^2)+x^3-31*x^2+30*x)*log(x-30)^4+((-4*x^4+120*x^
3)*exp(x^2)-x^3+30*x^2)*log(x-30)^2-2*x^3*log(x-30)+(2*x^4-60*x^3)*exp(x^2))/((x-30)*log(x-30)^4*log(x)^2+((2*
x^2-60*x)*log(x-30)^4+(-2*x^2+60*x)*log(x-30)^2)*log(x)+(x^3-30*x^2)*log(x-30)^4+(-2*x^3+60*x^2)*log(x-30)^2+x
^3-30*x^2),x, algorithm="giac")

[Out]

(x^2*log(x - 30)^2 + x*e^(x^2)*log(x - 30)^2 + e^(x^2)*log(x - 30)^2*log(x) - x*e^(x^2))/(x*log(x - 30)^2 + lo
g(x - 30)^2*log(x) - x)

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maple [B]  time = 0.08, size = 59, normalized size = 2.03

method	result	size
risch	\(\frac {x^{2}+{\mathrm e}^{x^{2}} x +{\mathrm e}^{x^{2}} \ln \relax (x )}{x +\ln \relax (x )}+\frac {x^{3}}{\left (x +\ln \relax (x )\right ) \left (\ln \left (x -30\right )^{2} \ln \relax (x )+x \ln \left (x -30\right )^{2}-x \right )}\)	\(59\)

Verification of antiderivative is not currently implemented for this CAS.

[In]

int(((2*x^2-60*x)*exp(x^2)*ln(x-30)^4*ln(x)^2+(((4*x^3-120*x^2)*exp(x^2)+2*x^2-60*x)*ln(x-30)^4+(-4*x^3+120*x^
2)*exp(x^2)*ln(x-30)^2)*ln(x)+((2*x^4-60*x^3)*exp(x^2)+x^3-31*x^2+30*x)*ln(x-30)^4+((-4*x^4+120*x^3)*exp(x^2)-
x^3+30*x^2)*ln(x-30)^2-2*x^3*ln(x-30)+(2*x^4-60*x^3)*exp(x^2))/((x-30)*ln(x-30)^4*ln(x)^2+((2*x^2-60*x)*ln(x-3
0)^4+(-2*x^2+60*x)*ln(x-30)^2)*ln(x)+(x^3-30*x^2)*ln(x-30)^4+(-2*x^3+60*x^2)*ln(x-30)^2+x^3-30*x^2),x,method=_
RETURNVERBOSE)

[Out]

(x^2+exp(x^2)*x+exp(x^2)*ln(x))/(x+ln(x))+x^3/(x+ln(x))/(ln(x-30)^2*ln(x)+x*ln(x-30)^2-x)

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maxima [B]  time = 0.46, size = 49, normalized size = 1.69 \begin {gather*} \frac {x^{2} \log \left (x - 30\right )^{2} + {\left ({\left (x + \log \relax (x)\right )} \log \left (x - 30\right )^{2} - x\right )} e^{\left (x^{2}\right )}}{{\left (x + \log \relax (x)\right )} \log \left (x - 30\right )^{2} - x} \end {gather*}

Verification of antiderivative is not currently implemented for this CAS.

[In]

integrate(((2*x^2-60*x)*exp(x^2)*log(x-30)^4*log(x)^2+(((4*x^3-120*x^2)*exp(x^2)+2*x^2-60*x)*log(x-30)^4+(-4*x
^3+120*x^2)*exp(x^2)*log(x-30)^2)*log(x)+((2*x^4-60*x^3)*exp(x^2)+x^3-31*x^2+30*x)*log(x-30)^4+((-4*x^4+120*x^
3)*exp(x^2)-x^3+30*x^2)*log(x-30)^2-2*x^3*log(x-30)+(2*x^4-60*x^3)*exp(x^2))/((x-30)*log(x-30)^4*log(x)^2+((2*
x^2-60*x)*log(x-30)^4+(-2*x^2+60*x)*log(x-30)^2)*log(x)+(x^3-30*x^2)*log(x-30)^4+(-2*x^3+60*x^2)*log(x-30)^2+x
^3-30*x^2),x, algorithm="maxima")

[Out]

(x^2*log(x - 30)^2 + ((x + log(x))*log(x - 30)^2 - x)*e^(x^2))/((x + log(x))*log(x - 30)^2 - x)

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mupad [B]  time = 6.17, size = 317, normalized size = 10.93 \begin {gather*} 2\,x+{\mathrm {e}}^{x^2}+\frac {2}{x+1}-\frac {\frac {x^2\,\left (x-1\right )}{x+1}+\frac {2\,x^2\,\ln \relax (x)}{x+1}}{x+\ln \relax (x)}+\frac {x^2\,{\left (30\,x-x^2\right )}^2\,\left (4\,x^4+12\,x^3\,\ln \relax (x)+11\,x^2\,{\ln \relax (x)}^2+2\,x^2\,\ln \relax (x)-x^2+4\,x\,{\ln \relax (x)}^3+60\,x\,{\ln \relax (x)}^2-120\,x\,\ln \relax (x)+60\,x-900\,{\ln \relax (x)}^2+1800\,\ln \relax (x)-900\right )}{\left (x-{\ln \left (x-30\right )}^2\,\left (x+\ln \relax (x)\right )\right )\,\left (x-30\right )\,\left (-4\,x^7-16\,x^6\,\ln \relax (x)+120\,x^6-23\,x^5\,{\ln \relax (x)}^2+478\,x^5\,\ln \relax (x)+x^5-15\,x^4\,{\ln \relax (x)}^3+628\,x^4\,{\ln \relax (x)}^2+181\,x^4\,\ln \relax (x)-90\,x^4-4\,x^3\,{\ln \relax (x)}^4+390\,x^3\,{\ln \relax (x)}^3+2880\,x^3\,{\ln \relax (x)}^2-5490\,x^3\,\ln \relax (x)+2700\,x^3+120\,x^2\,{\ln \relax (x)}^4+2700\,x^2\,{\ln \relax (x)}^3-32400\,x^2\,{\ln \relax (x)}^2+56700\,x^2\,\ln \relax (x)-27000\,x^2-27000\,x\,{\ln \relax (x)}^3+54000\,x\,{\ln \relax (x)}^2-27000\,x\,\ln \relax (x)\right )} \end {gather*}

Verification of antiderivative is not currently implemented for this CAS.

[In]

int(-(exp(x^2)*(60*x^3 - 2*x^4) - log(x - 30)^2*(exp(x^2)*(120*x^3 - 4*x^4) + 30*x^2 - x^3) + 2*x^3*log(x - 30
) + log(x)*(log(x - 30)^4*(60*x + exp(x^2)*(120*x^2 - 4*x^3) - 2*x^2) - log(x - 30)^2*exp(x^2)*(120*x^2 - 4*x^
3)) - log(x - 30)^4*(30*x - exp(x^2)*(60*x^3 - 2*x^4) - 31*x^2 + x^3) + log(x - 30)^4*exp(x^2)*log(x)^2*(60*x
- 2*x^2))/(log(x)*(log(x - 30)^2*(60*x - 2*x^2) - log(x - 30)^4*(60*x - 2*x^2)) - log(x - 30)^4*(30*x^2 - x^3)
+ log(x - 30)^2*(60*x^2 - 2*x^3) - 30*x^2 + x^3 + log(x - 30)^4*log(x)^2*(x - 30)),x)

[Out]

2*x + exp(x^2) + 2/(x + 1) - ((x^2*(x - 1))/(x + 1) + (2*x^2*log(x))/(x + 1))/(x + log(x)) + (x^2*(30*x - x^2)
^2*(60*x + 1800*log(x) + 60*x*log(x)^2 + 2*x^2*log(x) + 4*x*log(x)^3 + 12*x^3*log(x) - 900*log(x)^2 + 11*x^2*l
og(x)^2 - 120*x*log(x) - x^2 + 4*x^4 - 900))/((x - log(x - 30)^2*(x + log(x)))*(x - 30)*(54000*x*log(x)^2 + 56
700*x^2*log(x) - 27000*x*log(x)^3 - 5490*x^3*log(x) + 181*x^4*log(x) + 478*x^5*log(x) - 16*x^6*log(x) - 32400*
x^2*log(x)^2 + 2700*x^2*log(x)^3 + 2880*x^3*log(x)^2 + 120*x^2*log(x)^4 + 390*x^3*log(x)^3 + 628*x^4*log(x)^2
- 4*x^3*log(x)^4 - 15*x^4*log(x)^3 - 23*x^5*log(x)^2 - 27000*x*log(x) - 27000*x^2 + 2700*x^3 - 90*x^4 + x^5 +
120*x^6 - 4*x^7))

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sympy [B]  time = 0.85, size = 46, normalized size = 1.59 \begin {gather*} \frac {x^{3}}{- x^{2} - x \log {\relax (x )} + \left (x^{2} + 2 x \log {\relax (x )} + \log {\relax (x )}^{2}\right ) \log {\left (x - 30 \right )}^{2}} + \frac {x^{2}}{x + \log {\relax (x )}} + e^{x^{2}} \end {gather*}

Verification of antiderivative is not currently implemented for this CAS.

[In]

integrate(((2*x**2-60*x)*exp(x**2)*ln(x-30)**4*ln(x)**2+(((4*x**3-120*x**2)*exp(x**2)+2*x**2-60*x)*ln(x-30)**4
+(-4*x**3+120*x**2)*exp(x**2)*ln(x-30)**2)*ln(x)+((2*x**4-60*x**3)*exp(x**2)+x**3-31*x**2+30*x)*ln(x-30)**4+((
-4*x**4+120*x**3)*exp(x**2)-x**3+30*x**2)*ln(x-30)**2-2*x**3*ln(x-30)+(2*x**4-60*x**3)*exp(x**2))/((x-30)*ln(x
-30)**4*ln(x)**2+((2*x**2-60*x)*ln(x-30)**4+(-2*x**2+60*x)*ln(x-30)**2)*ln(x)+(x**3-30*x**2)*ln(x-30)**4+(-2*x
**3+60*x**2)*ln(x-30)**2+x**3-30*x**2),x)

[Out]

x**3/(-x**2 - x*log(x) + (x**2 + 2*x*log(x) + log(x)**2)*log(x - 30)**2) + x**2/(x + log(x)) + exp(x**2)

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