3.34.41 \(\int \frac {1800-600 x-550 x^2+100 x^3+50 x^4+(600-100 x-100 x^2) \log (x)+50 \log ^2(x)+(1500-250 x+50 x^2-50 x^3-50 x^4+(550-50 x) \log (x)+50 \log ^2(x)) \log (x^2)+x^3 \log ^2(x^2)}{x^3 \log ^2(x^2)} \, dx\)

Optimal. Leaf size=26 \[ x-\frac {25 \left (x-\frac {6-x+\log (x)}{x}\right )^2}{\log \left (x^2\right )} \]

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Rubi [F]  time = 1.40, 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 {1800-600 x-550 x^2+100 x^3+50 x^4+\left (600-100 x-100 x^2\right ) \log (x)+50 \log ^2(x)+\left (1500-250 x+50 x^2-50 x^3-50 x^4+(550-50 x) \log (x)+50 \log ^2(x)\right ) \log \left (x^2\right )+x^3 \log ^2\left (x^2\right )}{x^3 \log ^2\left (x^2\right )} \, dx \end {gather*}

Verification is not applicable to the result.

[In]

Int[(1800 - 600*x - 550*x^2 + 100*x^3 + 50*x^4 + (600 - 100*x - 100*x^2)*Log[x] + 50*Log[x]^2 + (1500 - 250*x
+ 50*x^2 - 50*x^3 - 50*x^4 + (550 - 50*x)*Log[x] + 50*Log[x]^2)*Log[x^2] + x^3*Log[x^2]^2)/(x^3*Log[x^2]^2),x]

[Out]

25/(2*x^2) + x - 25*ExpIntegralEi[-Log[x^2]]*Log[x] + 275/Log[x^2] - 900/(x^2*Log[x^2]) + 300/(x*Log[x^2]) - (
50*x)/Log[x^2] - (25*x^2)/Log[x^2] + (50*Log[x])/Log[x^2] - (300*Log[x])/(x^2*Log[x^2]) + (50*Log[x])/(x*Log[x
^2]) + (25*ExpIntegralEi[-Log[x^2]]*Log[x^2])/2 + 50*Defer[Int][Log[x]^2/(x^3*Log[x^2]^2), x] + 50*Defer[Int][
Log[x]^2/(x^3*Log[x^2]), x]

Rubi steps

\begin {gather*} \begin {aligned} \text {integral} &=\int \left (1+\frac {50 \left (-6+x+x^2-\log (x)\right )^2}{x^3 \log ^2\left (x^2\right )}-\frac {50 \left (-6+x+x^2-\log (x)\right ) \left (5+x^2+\log (x)\right )}{x^3 \log \left (x^2\right )}\right ) \, dx\\ &=x+50 \int \frac {\left (-6+x+x^2-\log (x)\right )^2}{x^3 \log ^2\left (x^2\right )} \, dx-50 \int \frac {\left (-6+x+x^2-\log (x)\right ) \left (5+x^2+\log (x)\right )}{x^3 \log \left (x^2\right )} \, dx\\ &=x+50 \int \left (\frac {2}{\log ^2\left (x^2\right )}+\frac {36}{x^3 \log ^2\left (x^2\right )}-\frac {12}{x^2 \log ^2\left (x^2\right )}-\frac {11}{x \log ^2\left (x^2\right )}+\frac {x}{\log ^2\left (x^2\right )}+\frac {12 \log (x)}{x^3 \log ^2\left (x^2\right )}-\frac {2 \log (x)}{x^2 \log ^2\left (x^2\right )}-\frac {2 \log (x)}{x \log ^2\left (x^2\right )}+\frac {\log ^2(x)}{x^3 \log ^2\left (x^2\right )}\right ) \, dx-50 \int \left (\frac {1}{\log \left (x^2\right )}-\frac {30}{x^3 \log \left (x^2\right )}+\frac {5}{x^2 \log \left (x^2\right )}-\frac {1}{x \log \left (x^2\right )}+\frac {x}{\log \left (x^2\right )}-\frac {11 \log (x)}{x^3 \log \left (x^2\right )}+\frac {\log (x)}{x^2 \log \left (x^2\right )}-\frac {\log ^2(x)}{x^3 \log \left (x^2\right )}\right ) \, dx\\ &=x+50 \int \frac {x}{\log ^2\left (x^2\right )} \, dx+50 \int \frac {\log ^2(x)}{x^3 \log ^2\left (x^2\right )} \, dx-50 \int \frac {1}{\log \left (x^2\right )} \, dx+50 \int \frac {1}{x \log \left (x^2\right )} \, dx-50 \int \frac {x}{\log \left (x^2\right )} \, dx-50 \int \frac {\log (x)}{x^2 \log \left (x^2\right )} \, dx+50 \int \frac {\log ^2(x)}{x^3 \log \left (x^2\right )} \, dx+100 \int \frac {1}{\log ^2\left (x^2\right )} \, dx-100 \int \frac {\log (x)}{x^2 \log ^2\left (x^2\right )} \, dx-100 \int \frac {\log (x)}{x \log ^2\left (x^2\right )} \, dx-250 \int \frac {1}{x^2 \log \left (x^2\right )} \, dx-550 \int \frac {1}{x \log ^2\left (x^2\right )} \, dx+550 \int \frac {\log (x)}{x^3 \log \left (x^2\right )} \, dx-600 \int \frac {1}{x^2 \log ^2\left (x^2\right )} \, dx+600 \int \frac {\log (x)}{x^3 \log ^2\left (x^2\right )} \, dx+1500 \int \frac {1}{x^3 \log \left (x^2\right )} \, dx+1800 \int \frac {1}{x^3 \log ^2\left (x^2\right )} \, dx\\ &=x-25 \text {Ei}\left (-\log \left (x^2\right )\right ) \log (x)-\frac {900}{x^2 \log \left (x^2\right )}+\frac {300}{x \log \left (x^2\right )}-\frac {50 x}{\log \left (x^2\right )}-\frac {25 x^2}{\log \left (x^2\right )}+\frac {50 \log (x)}{\log \left (x^2\right )}-\frac {300 \log (x)}{x^2 \log \left (x^2\right )}+\frac {50 \log (x)}{x \log \left (x^2\right )}+25 \operatorname {Subst}\left (\int \frac {1}{x} \, dx,x,\log \left (x^2\right )\right )-25 \operatorname {Subst}\left (\int \frac {1}{\log (x)} \, dx,x,x^2\right )+50 \int \frac {\text {Ei}\left (-\frac {1}{2} \log \left (x^2\right )\right )}{2 \sqrt {x^2}} \, dx+50 \int \frac {\log ^2(x)}{x^3 \log ^2\left (x^2\right )} \, dx+50 \int \frac {1}{\log \left (x^2\right )} \, dx+50 \int \frac {x}{\log \left (x^2\right )} \, dx+50 \int \frac {\log ^2(x)}{x^3 \log \left (x^2\right )} \, dx+100 \int \left (-\frac {\text {Ei}\left (-\frac {1}{2} \log \left (x^2\right )\right )}{4 \sqrt {x^2}}-\frac {1}{2 x^2 \log \left (x^2\right )}\right ) \, dx+100 \int -\frac {1}{2 x \log \left (x^2\right )} \, dx-275 \operatorname {Subst}\left (\int \frac {1}{x^2} \, dx,x,\log \left (x^2\right )\right )+300 \int \frac {1}{x^2 \log \left (x^2\right )} \, dx-550 \int \frac {\text {Ei}\left (-\log \left (x^2\right )\right )}{2 x} \, dx-600 \int \frac {-x^2 \text {Ei}\left (-\log \left (x^2\right )\right )-\frac {1}{\log \left (x^2\right )}}{2 x^3} \, dx+750 \operatorname {Subst}\left (\int \frac {e^{-x}}{x} \, dx,x,\log \left (x^2\right )\right )-1800 \int \frac {1}{x^3 \log \left (x^2\right )} \, dx-\frac {(25 x) \operatorname {Subst}\left (\int \frac {e^{x/2}}{x} \, dx,x,\log \left (x^2\right )\right )}{\sqrt {x^2}}-\frac {\left (125 \sqrt {x^2}\right ) \operatorname {Subst}\left (\int \frac {e^{-x/2}}{x} \, dx,x,\log \left (x^2\right )\right )}{x}\\ &=x+750 \text {Ei}\left (-\log \left (x^2\right )\right )-\frac {125 \sqrt {x^2} \text {Ei}\left (-\frac {1}{2} \log \left (x^2\right )\right )}{x}-\frac {25 x \text {Ei}\left (\frac {\log \left (x^2\right )}{2}\right )}{\sqrt {x^2}}-25 \text {Ei}\left (-\log \left (x^2\right )\right ) \log (x)+\frac {275}{\log \left (x^2\right )}-\frac {900}{x^2 \log \left (x^2\right )}+\frac {300}{x \log \left (x^2\right )}-\frac {50 x}{\log \left (x^2\right )}-\frac {25 x^2}{\log \left (x^2\right )}+\frac {50 \log (x)}{\log \left (x^2\right )}-\frac {300 \log (x)}{x^2 \log \left (x^2\right )}+\frac {50 \log (x)}{x \log \left (x^2\right )}+25 \log \left (\log \left (x^2\right )\right )-25 \text {li}\left (x^2\right )+25 \operatorname {Subst}\left (\int \frac {1}{\log (x)} \, dx,x,x^2\right )+50 \int \frac {\log ^2(x)}{x^3 \log ^2\left (x^2\right )} \, dx-50 \int \frac {1}{x^2 \log \left (x^2\right )} \, dx-50 \int \frac {1}{x \log \left (x^2\right )} \, dx+50 \int \frac {\log ^2(x)}{x^3 \log \left (x^2\right )} \, dx-275 \int \frac {\text {Ei}\left (-\log \left (x^2\right )\right )}{x} \, dx-300 \int \frac {-x^2 \text {Ei}\left (-\log \left (x^2\right )\right )-\frac {1}{\log \left (x^2\right )}}{x^3} \, dx-900 \operatorname {Subst}\left (\int \frac {e^{-x}}{x} \, dx,x,\log \left (x^2\right )\right )+\frac {(25 x) \operatorname {Subst}\left (\int \frac {e^{x/2}}{x} \, dx,x,\log \left (x^2\right )\right )}{\sqrt {x^2}}+\frac {\left (150 \sqrt {x^2}\right ) \operatorname {Subst}\left (\int \frac {e^{-x/2}}{x} \, dx,x,\log \left (x^2\right )\right )}{x}\\ &=x-150 \text {Ei}\left (-\log \left (x^2\right )\right )+\frac {25 \sqrt {x^2} \text {Ei}\left (-\frac {1}{2} \log \left (x^2\right )\right )}{x}-25 \text {Ei}\left (-\log \left (x^2\right )\right ) \log (x)+\frac {275}{\log \left (x^2\right )}-\frac {900}{x^2 \log \left (x^2\right )}+\frac {300}{x \log \left (x^2\right )}-\frac {50 x}{\log \left (x^2\right )}-\frac {25 x^2}{\log \left (x^2\right )}+\frac {50 \log (x)}{\log \left (x^2\right )}-\frac {300 \log (x)}{x^2 \log \left (x^2\right )}+\frac {50 \log (x)}{x \log \left (x^2\right )}+25 \log \left (\log \left (x^2\right )\right )-25 \operatorname {Subst}\left (\int \frac {1}{x} \, dx,x,\log \left (x^2\right )\right )+50 \int \frac {\log ^2(x)}{x^3 \log ^2\left (x^2\right )} \, dx+50 \int \frac {\log ^2(x)}{x^3 \log \left (x^2\right )} \, dx-\frac {275}{2} \operatorname {Subst}\left (\int \text {Ei}(-x) \, dx,x,\log \left (x^2\right )\right )-300 \int \left (-\frac {\text {Ei}\left (-\log \left (x^2\right )\right )}{x}-\frac {1}{x^3 \log \left (x^2\right )}\right ) \, dx-\frac {\left (25 \sqrt {x^2}\right ) \operatorname {Subst}\left (\int \frac {e^{-x/2}}{x} \, dx,x,\log \left (x^2\right )\right )}{x}\\ &=-\frac {275}{2 x^2}+x-150 \text {Ei}\left (-\log \left (x^2\right )\right )-25 \text {Ei}\left (-\log \left (x^2\right )\right ) \log (x)+\frac {275}{\log \left (x^2\right )}-\frac {900}{x^2 \log \left (x^2\right )}+\frac {300}{x \log \left (x^2\right )}-\frac {50 x}{\log \left (x^2\right )}-\frac {25 x^2}{\log \left (x^2\right )}+\frac {50 \log (x)}{\log \left (x^2\right )}-\frac {300 \log (x)}{x^2 \log \left (x^2\right )}+\frac {50 \log (x)}{x \log \left (x^2\right )}-\frac {275}{2} \text {Ei}\left (-\log \left (x^2\right )\right ) \log \left (x^2\right )+50 \int \frac {\log ^2(x)}{x^3 \log ^2\left (x^2\right )} \, dx+50 \int \frac {\log ^2(x)}{x^3 \log \left (x^2\right )} \, dx+300 \int \frac {\text {Ei}\left (-\log \left (x^2\right )\right )}{x} \, dx+300 \int \frac {1}{x^3 \log \left (x^2\right )} \, dx\\ &=-\frac {275}{2 x^2}+x-150 \text {Ei}\left (-\log \left (x^2\right )\right )-25 \text {Ei}\left (-\log \left (x^2\right )\right ) \log (x)+\frac {275}{\log \left (x^2\right )}-\frac {900}{x^2 \log \left (x^2\right )}+\frac {300}{x \log \left (x^2\right )}-\frac {50 x}{\log \left (x^2\right )}-\frac {25 x^2}{\log \left (x^2\right )}+\frac {50 \log (x)}{\log \left (x^2\right )}-\frac {300 \log (x)}{x^2 \log \left (x^2\right )}+\frac {50 \log (x)}{x \log \left (x^2\right )}-\frac {275}{2} \text {Ei}\left (-\log \left (x^2\right )\right ) \log \left (x^2\right )+50 \int \frac {\log ^2(x)}{x^3 \log ^2\left (x^2\right )} \, dx+50 \int \frac {\log ^2(x)}{x^3 \log \left (x^2\right )} \, dx+150 \operatorname {Subst}\left (\int \frac {e^{-x}}{x} \, dx,x,\log \left (x^2\right )\right )+150 \operatorname {Subst}\left (\int \text {Ei}(-x) \, dx,x,\log \left (x^2\right )\right )\\ &=\frac {25}{2 x^2}+x-25 \text {Ei}\left (-\log \left (x^2\right )\right ) \log (x)+\frac {275}{\log \left (x^2\right )}-\frac {900}{x^2 \log \left (x^2\right )}+\frac {300}{x \log \left (x^2\right )}-\frac {50 x}{\log \left (x^2\right )}-\frac {25 x^2}{\log \left (x^2\right )}+\frac {50 \log (x)}{\log \left (x^2\right )}-\frac {300 \log (x)}{x^2 \log \left (x^2\right )}+\frac {50 \log (x)}{x \log \left (x^2\right )}+\frac {25}{2} \text {Ei}\left (-\log \left (x^2\right )\right ) \log \left (x^2\right )+50 \int \frac {\log ^2(x)}{x^3 \log ^2\left (x^2\right )} \, dx+50 \int \frac {\log ^2(x)}{x^3 \log \left (x^2\right )} \, dx\\ \end {aligned} \end {gather*}

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Mathematica [A]  time = 0.06, size = 48, normalized size = 1.85 \begin {gather*} \frac {-25 \left (-6+x+x^2\right )^2+50 \left (-6+x+x^2\right ) \log (x)-25 \log ^2(x)+(-25+x) x^2 \log \left (x^2\right )}{x^2 \log \left (x^2\right )} \end {gather*}

Antiderivative was successfully verified.

[In]

Integrate[(1800 - 600*x - 550*x^2 + 100*x^3 + 50*x^4 + (600 - 100*x - 100*x^2)*Log[x] + 50*Log[x]^2 + (1500 -
250*x + 50*x^2 - 50*x^3 - 50*x^4 + (550 - 50*x)*Log[x] + 50*Log[x]^2)*Log[x^2] + x^3*Log[x^2]^2)/(x^3*Log[x^2]
^2),x]

[Out]

(-25*(-6 + x + x^2)^2 + 50*(-6 + x + x^2)*Log[x] - 25*Log[x]^2 + (-25 + x)*x^2*Log[x^2])/(x^2*Log[x^2])

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fricas [A]  time = 0.57, size = 47, normalized size = 1.81 \begin {gather*} -\frac {25 \, x^{4} + 50 \, x^{3} - 275 \, x^{2} - 2 \, {\left (x^{3} + 25 \, x - 150\right )} \log \relax (x) + 25 \, \log \relax (x)^{2} - 300 \, x + 900}{2 \, x^{2} \log \relax (x)} \end {gather*}

Verification of antiderivative is not currently implemented for this CAS.

[In]

integrate((x^3*log(x^2)^2+(50*log(x)^2+(-50*x+550)*log(x)-50*x^4-50*x^3+50*x^2-250*x+1500)*log(x^2)+50*log(x)^
2+(-100*x^2-100*x+600)*log(x)+50*x^4+100*x^3-550*x^2-600*x+1800)/x^3/log(x^2)^2,x, algorithm="fricas")

[Out]

-1/2*(25*x^4 + 50*x^3 - 275*x^2 - 2*(x^3 + 25*x - 150)*log(x) + 25*log(x)^2 - 300*x + 900)/(x^2*log(x))

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giac [A]  time = 0.27, size = 44, normalized size = 1.69 \begin {gather*} x + \frac {25 \, {\left (x - 6\right )}}{x^{2}} - \frac {25 \, \log \relax (x)}{2 \, x^{2}} - \frac {25 \, {\left (x^{4} + 2 \, x^{3} - 11 \, x^{2} - 12 \, x + 36\right )}}{2 \, x^{2} \log \relax (x)} \end {gather*}

Verification of antiderivative is not currently implemented for this CAS.

[In]

integrate((x^3*log(x^2)^2+(50*log(x)^2+(-50*x+550)*log(x)-50*x^4-50*x^3+50*x^2-250*x+1500)*log(x^2)+50*log(x)^
2+(-100*x^2-100*x+600)*log(x)+50*x^4+100*x^3-550*x^2-600*x+1800)/x^3/log(x^2)^2,x, algorithm="giac")

[Out]

x + 25*(x - 6)/x^2 - 25/2*log(x)/x^2 - 25/2*(x^4 + 2*x^3 - 11*x^2 - 12*x + 36)/(x^2*log(x))

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maple [C]  time = 0.10, size = 406, normalized size = 15.62

method	result	size
risch	\(-\frac {25 \ln \relax (x )}{2 x^{2}}+\frac {-25 i \pi \mathrm {csgn}\left (i x \right )^{2} \mathrm {csgn}\left (i x^{2}\right )+50 i \pi \,\mathrm {csgn}\left (i x \right ) \mathrm {csgn}\left (i x^{2}\right )^{2}-25 i \pi \mathrm {csgn}\left (i x^{2}\right )^{3}+8 x^{3}+200 x -1200}{8 x^{2}}-\frac {25 i \left (-\pi ^{2} \mathrm {csgn}\left (i x \right )^{4} \mathrm {csgn}\left (i x^{2}\right )^{2}+4 \pi ^{2} \mathrm {csgn}\left (i x \right )^{3} \mathrm {csgn}\left (i x^{2}\right )^{3}-6 \pi ^{2} \mathrm {csgn}\left (i x \right )^{2} \mathrm {csgn}\left (i x^{2}\right )^{4}+4 \pi ^{2} \mathrm {csgn}\left (i x \right ) \mathrm {csgn}\left (i x^{2}\right )^{5}-\pi ^{2} \mathrm {csgn}\left (i x^{2}\right )^{6}+16 i \pi \,x^{2} \mathrm {csgn}\left (i x \right ) \mathrm {csgn}\left (i x^{2}\right )^{2}+48 i \pi \mathrm {csgn}\left (i x \right )^{2} \mathrm {csgn}\left (i x^{2}\right )-8 i \pi \,x^{2} \mathrm {csgn}\left (i x \right )^{2} \mathrm {csgn}\left (i x^{2}\right )-8 i \pi x \mathrm {csgn}\left (i x^{2}\right )^{3}-96 i \pi \,\mathrm {csgn}\left (i x \right ) \mathrm {csgn}\left (i x^{2}\right )^{2}-8 i \pi \,x^{2} \mathrm {csgn}\left (i x^{2}\right )^{3}-8 i \pi x \mathrm {csgn}\left (i x \right )^{2} \mathrm {csgn}\left (i x^{2}\right )+48 i \pi \mathrm {csgn}\left (i x^{2}\right )^{3}+16 i \pi x \,\mathrm {csgn}\left (i x \right ) \mathrm {csgn}\left (i x^{2}\right )^{2}+16 x^{4}+32 x^{3}-176 x^{2}-192 x +576\right )}{8 x^{2} \left (\pi \mathrm {csgn}\left (i x \right )^{2} \mathrm {csgn}\left (i x^{2}\right )-2 \pi \,\mathrm {csgn}\left (i x \right ) \mathrm {csgn}\left (i x^{2}\right )^{2}+\pi \mathrm {csgn}\left (i x^{2}\right )^{3}+4 i \ln \relax (x )\right )}\)	\(406\)

Verification of antiderivative is not currently implemented for this CAS.

[In]

int((x^3*ln(x^2)^2+(50*ln(x)^2+(-50*x+550)*ln(x)-50*x^4-50*x^3+50*x^2-250*x+1500)*ln(x^2)+50*ln(x)^2+(-100*x^2
-100*x+600)*ln(x)+50*x^4+100*x^3-550*x^2-600*x+1800)/x^3/ln(x^2)^2,x,method=_RETURNVERBOSE)

[Out]

-25/2*ln(x)/x^2+1/8*(-25*I*Pi*csgn(I*x)^2*csgn(I*x^2)+50*I*Pi*csgn(I*x)*csgn(I*x^2)^2-25*I*Pi*csgn(I*x^2)^3+8*
x^3+200*x-1200)/x^2-25/8*I*(-Pi^2*csgn(I*x)^4*csgn(I*x^2)^2+4*Pi^2*csgn(I*x)^3*csgn(I*x^2)^3-6*Pi^2*csgn(I*x)^
2*csgn(I*x^2)^4+4*Pi^2*csgn(I*x)*csgn(I*x^2)^5-Pi^2*csgn(I*x^2)^6+16*I*Pi*x^2*csgn(I*x)*csgn(I*x^2)^2+48*I*Pi*
csgn(I*x)^2*csgn(I*x^2)-8*I*Pi*x^2*csgn(I*x)^2*csgn(I*x^2)-8*I*Pi*x*csgn(I*x^2)^3-96*I*Pi*csgn(I*x)*csgn(I*x^2
)^2-8*I*Pi*x^2*csgn(I*x^2)^3-8*I*Pi*x*csgn(I*x)^2*csgn(I*x^2)+48*I*Pi*csgn(I*x^2)^3+16*I*Pi*x*csgn(I*x)*csgn(I
*x^2)^2+16*x^4+32*x^3-176*x^2-192*x+576)/x^2/(Pi*csgn(I*x)^2*csgn(I*x^2)-2*Pi*csgn(I*x)*csgn(I*x^2)^2+Pi*csgn(
I*x^2)^3+4*I*ln(x))

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maxima [A]  time = 0.51, size = 40, normalized size = 1.54 \begin {gather*} x - \frac {25 \, {\left (x^{4} + 2 \, x^{3} - 11 \, x^{2} - 2 \, {\left (x - 6\right )} \log \relax (x) + \log \relax (x)^{2} - 12 \, x + 36\right )}}{2 \, x^{2} \log \relax (x)} \end {gather*}

Verification of antiderivative is not currently implemented for this CAS.

[In]

integrate((x^3*log(x^2)^2+(50*log(x)^2+(-50*x+550)*log(x)-50*x^4-50*x^3+50*x^2-250*x+1500)*log(x^2)+50*log(x)^
2+(-100*x^2-100*x+600)*log(x)+50*x^4+100*x^3-550*x^2-600*x+1800)/x^3/log(x^2)^2,x, algorithm="maxima")

[Out]

x - 25/2*(x^4 + 2*x^3 - 11*x^2 - 2*(x - 6)*log(x) + log(x)^2 - 12*x + 36)/(x^2*log(x))

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mupad [B]  time = 2.12, size = 103, normalized size = 3.96 \begin {gather*} x-\frac {50\,x}{\ln \left (x^2\right )}+\frac {275}{\ln \left (x^2\right )}+\frac {300}{x\,\ln \left (x^2\right )}-\frac {900}{x^2\,\ln \left (x^2\right )}-\frac {25\,x^2}{\ln \left (x^2\right )}+\frac {50\,\ln \relax (x)}{\ln \left (x^2\right )}-\frac {25\,{\ln \relax (x)}^2}{x^2\,\ln \left (x^2\right )}+\frac {50\,\ln \relax (x)}{x\,\ln \left (x^2\right )}-\frac {300\,\ln \relax (x)}{x^2\,\ln \left (x^2\right )} \end {gather*}

Verification of antiderivative is not currently implemented for this CAS.

[In]

int((50*log(x)^2 - 600*x - log(x^2)*(250*x - 50*log(x)^2 + log(x)*(50*x - 550) - 50*x^2 + 50*x^3 + 50*x^4 - 15
00) - log(x)*(100*x + 100*x^2 - 600) - 550*x^2 + 100*x^3 + 50*x^4 + x^3*log(x^2)^2 + 1800)/(x^3*log(x^2)^2),x)

[Out]

x - (50*x)/log(x^2) + 275/log(x^2) + 300/(x*log(x^2)) - 900/(x^2*log(x^2)) - (25*x^2)/log(x^2) + (50*log(x))/l
og(x^2) - (25*log(x)^2)/(x^2*log(x^2)) + (50*log(x))/(x*log(x^2)) - (300*log(x))/(x^2*log(x^2))

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sympy [A]  time = 0.32, size = 48, normalized size = 1.85 \begin {gather*} x + \frac {25 x - 150}{x^{2}} + \frac {- 25 x^{4} - 50 x^{3} + 275 x^{2} + 300 x - 900}{2 x^{2} \log {\relax (x )}} - \frac {25 \log {\relax (x )}}{2 x^{2}} \end {gather*}

Verification of antiderivative is not currently implemented for this CAS.

[In]

integrate((x**3*ln(x**2)**2+(50*ln(x)**2+(-50*x+550)*ln(x)-50*x**4-50*x**3+50*x**2-250*x+1500)*ln(x**2)+50*ln(
x)**2+(-100*x**2-100*x+600)*ln(x)+50*x**4+100*x**3-550*x**2-600*x+1800)/x**3/ln(x**2)**2,x)

[Out]

x + (25*x - 150)/x**2 + (-25*x**4 - 50*x**3 + 275*x**2 + 300*x - 900)/(2*x**2*log(x)) - 25*log(x)/(2*x**2)

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