3.51.33 \(\int \frac {e^{-x^2+x^4} (x+6 \log (4 x+5 x^2+x^3)) (24+64 x+23 x^2-7 x^3-10 x^4+14 x^5+20 x^6+4 x^7+(-48 x^2-60 x^3+84 x^4+120 x^5+24 x^6) \log (4 x+5 x^2+x^3))}{4 x^2+5 x^3+x^4+(24 x+30 x^2+6 x^3) \log (4 x+5 x^2+x^3)} \, dx\)

Optimal. Leaf size=26 \[ e^{-x^2+x^4} \left (x+6 \log \left ((4+x) \left (x+x^2\right )\right )\right ) \]

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Rubi [F]  time = 9.44, 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+x^4} \left (x+6 \log \left (4 x+5 x^2+x^3\right )\right ) \left (24+64 x+23 x^2-7 x^3-10 x^4+14 x^5+20 x^6+4 x^7+\left (-48 x^2-60 x^3+84 x^4+120 x^5+24 x^6\right ) \log \left (4 x+5 x^2+x^3\right )\right )}{4 x^2+5 x^3+x^4+\left (24 x+30 x^2+6 x^3\right ) \log \left (4 x+5 x^2+x^3\right )} \, dx \end {gather*}

Verification is not applicable to the result.

[In]

Int[(E^(-x^2 + x^4)*(x + 6*Log[4*x + 5*x^2 + x^3])*(24 + 64*x + 23*x^2 - 7*x^3 - 10*x^4 + 14*x^5 + 20*x^6 + 4*
x^7 + (-48*x^2 - 60*x^3 + 84*x^4 + 120*x^5 + 24*x^6)*Log[4*x + 5*x^2 + x^3]))/(4*x^2 + 5*x^3 + x^4 + (24*x + 3
0*x^2 + 6*x^3)*Log[4*x + 5*x^2 + x^3]),x]

[Out]

6*E^(-x^2 + x^4)*Log[x*(4 + 5*x + x^2)] + Defer[Int][E^(-x^2 + x^4), x] - (128*Defer[Int][E^(-x^2 + x^4)/(-2 -
2*x), x])/3 - 2*Defer[Int][E^(-x^2 + x^4)*x^2, x] + 4*Defer[Int][E^(-x^2 + x^4)*x^4, x] - 14*Defer[Int][E^(-x
^2 + x^4)/(1 + x), x] - 4*Defer[Int][E^(-x^2 + x^4)/(4 + x), x] - (44*Defer[Int][E^(-x^2 + x^4)/(2 + 2*x), x])
/3 + 8*Defer[Int][E^(-x^2 + x^4)/(8 + 2*x), x]

Rubi steps

\begin {gather*} \begin {aligned} \text {integral} &=\int \frac {e^{-x^2+x^4} \left (24+64 x+23 x^2-7 x^3-10 x^4+14 x^5+20 x^6+4 x^7+12 x^2 \left (-4-5 x+7 x^2+10 x^3+2 x^4\right ) \log \left (x \left (4+5 x+x^2\right )\right )\right )}{x \left (4+5 x+x^2\right )} \, dx\\ &=\int \left (\frac {64 e^{-x^2+x^4}}{4+5 x+x^2}+\frac {24 e^{-x^2+x^4}}{x \left (4+5 x+x^2\right )}+\frac {23 e^{-x^2+x^4} x}{4+5 x+x^2}-\frac {7 e^{-x^2+x^4} x^2}{4+5 x+x^2}-\frac {10 e^{-x^2+x^4} x^3}{4+5 x+x^2}+\frac {14 e^{-x^2+x^4} x^4}{4+5 x+x^2}+\frac {20 e^{-x^2+x^4} x^5}{4+5 x+x^2}+\frac {4 e^{-x^2+x^4} x^6}{4+5 x+x^2}+12 e^{-x^2+x^4} x \left (-1+2 x^2\right ) \log \left (x \left (4+5 x+x^2\right )\right )\right ) \, dx\\ &=4 \int \frac {e^{-x^2+x^4} x^6}{4+5 x+x^2} \, dx-7 \int \frac {e^{-x^2+x^4} x^2}{4+5 x+x^2} \, dx-10 \int \frac {e^{-x^2+x^4} x^3}{4+5 x+x^2} \, dx+12 \int e^{-x^2+x^4} x \left (-1+2 x^2\right ) \log \left (x \left (4+5 x+x^2\right )\right ) \, dx+14 \int \frac {e^{-x^2+x^4} x^4}{4+5 x+x^2} \, dx+20 \int \frac {e^{-x^2+x^4} x^5}{4+5 x+x^2} \, dx+23 \int \frac {e^{-x^2+x^4} x}{4+5 x+x^2} \, dx+24 \int \frac {e^{-x^2+x^4}}{x \left (4+5 x+x^2\right )} \, dx+64 \int \frac {e^{-x^2+x^4}}{4+5 x+x^2} \, dx\\ &=6 e^{-x^2+x^4} \log \left (x \left (4+5 x+x^2\right )\right )+4 \int \left (341 e^{-x^2+x^4}-85 e^{-x^2+x^4} x+21 e^{-x^2+x^4} x^2-5 e^{-x^2+x^4} x^3+e^{-x^2+x^4} x^4-\frac {e^{-x^2+x^4} (1364+1365 x)}{4+5 x+x^2}\right ) \, dx-7 \int \left (e^{-x^2+x^4}-\frac {e^{-x^2+x^4} (4+5 x)}{4+5 x+x^2}\right ) \, dx-10 \int \left (-5 e^{-x^2+x^4}+e^{-x^2+x^4} x+\frac {e^{-x^2+x^4} (20+21 x)}{4+5 x+x^2}\right ) \, dx-12 \int \frac {e^{-x^2+x^4} \left (4+10 x+3 x^2\right )}{2 x \left (4+5 x+x^2\right )} \, dx+14 \int \left (21 e^{-x^2+x^4}-5 e^{-x^2+x^4} x+e^{-x^2+x^4} x^2-\frac {e^{-x^2+x^4} (84+85 x)}{4+5 x+x^2}\right ) \, dx+20 \int \left (-85 e^{-x^2+x^4}+21 e^{-x^2+x^4} x-5 e^{-x^2+x^4} x^2+e^{-x^2+x^4} x^3+\frac {e^{-x^2+x^4} (340+341 x)}{4+5 x+x^2}\right ) \, dx+23 \int \left (-\frac {2 e^{-x^2+x^4}}{3 (2+2 x)}+\frac {8 e^{-x^2+x^4}}{3 (8+2 x)}\right ) \, dx+24 \int \left (\frac {e^{-x^2+x^4}}{4 x}-\frac {e^{-x^2+x^4}}{3 (1+x)}+\frac {e^{-x^2+x^4}}{12 (4+x)}\right ) \, dx+64 \int \left (-\frac {2 e^{-x^2+x^4}}{3 (-2-2 x)}-\frac {2 e^{-x^2+x^4}}{3 (8+2 x)}\right ) \, dx\\ &=6 e^{-x^2+x^4} \log \left (x \left (4+5 x+x^2\right )\right )+2 \int \frac {e^{-x^2+x^4}}{4+x} \, dx+4 \int e^{-x^2+x^4} x^4 \, dx-4 \int \frac {e^{-x^2+x^4} (1364+1365 x)}{4+5 x+x^2} \, dx+6 \int \frac {e^{-x^2+x^4}}{x} \, dx-6 \int \frac {e^{-x^2+x^4} \left (4+10 x+3 x^2\right )}{x \left (4+5 x+x^2\right )} \, dx-7 \int e^{-x^2+x^4} \, dx+7 \int \frac {e^{-x^2+x^4} (4+5 x)}{4+5 x+x^2} \, dx-8 \int \frac {e^{-x^2+x^4}}{1+x} \, dx-10 \int e^{-x^2+x^4} x \, dx-10 \int \frac {e^{-x^2+x^4} (20+21 x)}{4+5 x+x^2} \, dx+14 \int e^{-x^2+x^4} x^2 \, dx-14 \int \frac {e^{-x^2+x^4} (84+85 x)}{4+5 x+x^2} \, dx-\frac {46}{3} \int \frac {e^{-x^2+x^4}}{2+2 x} \, dx+20 \int \frac {e^{-x^2+x^4} (340+341 x)}{4+5 x+x^2} \, dx-\frac {128}{3} \int \frac {e^{-x^2+x^4}}{-2-2 x} \, dx-\frac {128}{3} \int \frac {e^{-x^2+x^4}}{8+2 x} \, dx+50 \int e^{-x^2+x^4} \, dx+\frac {184}{3} \int \frac {e^{-x^2+x^4}}{8+2 x} \, dx-70 \int e^{-x^2+x^4} x \, dx+84 \int e^{-x^2+x^4} x^2 \, dx-100 \int e^{-x^2+x^4} x^2 \, dx+294 \int e^{-x^2+x^4} \, dx-340 \int e^{-x^2+x^4} x \, dx+420 \int e^{-x^2+x^4} x \, dx+1364 \int e^{-x^2+x^4} \, dx-1700 \int e^{-x^2+x^4} \, dx\\ &=6 e^{-x^2+x^4} \log \left (x \left (4+5 x+x^2\right )\right )+2 \int \frac {e^{-x^2+x^4}}{4+x} \, dx+3 \operatorname {Subst}\left (\int \frac {e^{-x+x^2}}{x} \, dx,x,x^2\right )+4 \int e^{-x^2+x^4} x^4 \, dx-4 \int \left (-\frac {2 e^{-x^2+x^4}}{3 (2+2 x)}+\frac {8192 e^{-x^2+x^4}}{3 (8+2 x)}\right ) \, dx-5 \operatorname {Subst}\left (\int e^{-x+x^2} \, dx,x,x^2\right )-6 \int \left (\frac {e^{-x^2+x^4}}{x}+\frac {e^{-x^2+x^4}}{1+x}+\frac {e^{-x^2+x^4}}{4+x}\right ) \, dx-7 \int e^{-x^2+x^4} \, dx+7 \int \left (-\frac {2 e^{-x^2+x^4}}{3 (2+2 x)}+\frac {32 e^{-x^2+x^4}}{3 (8+2 x)}\right ) \, dx-8 \int \frac {e^{-x^2+x^4}}{1+x} \, dx-10 \int \left (-\frac {2 e^{-x^2+x^4}}{3 (2+2 x)}+\frac {128 e^{-x^2+x^4}}{3 (8+2 x)}\right ) \, dx+14 \int e^{-x^2+x^4} x^2 \, dx-14 \int \left (-\frac {2 e^{-x^2+x^4}}{3 (2+2 x)}+\frac {512 e^{-x^2+x^4}}{3 (8+2 x)}\right ) \, dx-\frac {46}{3} \int \frac {e^{-x^2+x^4}}{2+2 x} \, dx+20 \int \left (-\frac {2 e^{-x^2+x^4}}{3 (2+2 x)}+\frac {2048 e^{-x^2+x^4}}{3 (8+2 x)}\right ) \, dx-35 \operatorname {Subst}\left (\int e^{-x+x^2} \, dx,x,x^2\right )-\frac {128}{3} \int \frac {e^{-x^2+x^4}}{-2-2 x} \, dx-\frac {128}{3} \int \frac {e^{-x^2+x^4}}{8+2 x} \, dx+50 \int e^{-x^2+x^4} \, dx+\frac {184}{3} \int \frac {e^{-x^2+x^4}}{8+2 x} \, dx+84 \int e^{-x^2+x^4} x^2 \, dx-100 \int e^{-x^2+x^4} x^2 \, dx-170 \operatorname {Subst}\left (\int e^{-x+x^2} \, dx,x,x^2\right )+210 \operatorname {Subst}\left (\int e^{-x+x^2} \, dx,x,x^2\right )+294 \int e^{-x^2+x^4} \, dx+1364 \int e^{-x^2+x^4} \, dx-1700 \int e^{-x^2+x^4} \, dx\\ &=6 e^{-x^2+x^4} \log \left (x \left (4+5 x+x^2\right )\right )+2 \int \frac {e^{-x^2+x^4}}{4+x} \, dx+\frac {8}{3} \int \frac {e^{-x^2+x^4}}{2+2 x} \, dx+3 \operatorname {Subst}\left (\int \frac {e^{-x+x^2}}{x} \, dx,x,x^2\right )+4 \int e^{-x^2+x^4} x^4 \, dx-\frac {14}{3} \int \frac {e^{-x^2+x^4}}{2+2 x} \, dx-6 \int \frac {e^{-x^2+x^4}}{x} \, dx-6 \int \frac {e^{-x^2+x^4}}{1+x} \, dx-6 \int \frac {e^{-x^2+x^4}}{4+x} \, dx+\frac {20}{3} \int \frac {e^{-x^2+x^4}}{2+2 x} \, dx-7 \int e^{-x^2+x^4} \, dx-8 \int \frac {e^{-x^2+x^4}}{1+x} \, dx+\frac {28}{3} \int \frac {e^{-x^2+x^4}}{2+2 x} \, dx-\frac {40}{3} \int \frac {e^{-x^2+x^4}}{2+2 x} \, dx+14 \int e^{-x^2+x^4} x^2 \, dx-\frac {46}{3} \int \frac {e^{-x^2+x^4}}{2+2 x} \, dx-\frac {128}{3} \int \frac {e^{-x^2+x^4}}{-2-2 x} \, dx-\frac {128}{3} \int \frac {e^{-x^2+x^4}}{8+2 x} \, dx+50 \int e^{-x^2+x^4} \, dx+\frac {184}{3} \int \frac {e^{-x^2+x^4}}{8+2 x} \, dx+\frac {224}{3} \int \frac {e^{-x^2+x^4}}{8+2 x} \, dx+84 \int e^{-x^2+x^4} x^2 \, dx-100 \int e^{-x^2+x^4} x^2 \, dx+294 \int e^{-x^2+x^4} \, dx-\frac {1280}{3} \int \frac {e^{-x^2+x^4}}{8+2 x} \, dx+1364 \int e^{-x^2+x^4} \, dx-1700 \int e^{-x^2+x^4} \, dx-\frac {7168}{3} \int \frac {e^{-x^2+x^4}}{8+2 x} \, dx-\frac {32768}{3} \int \frac {e^{-x^2+x^4}}{8+2 x} \, dx+\frac {40960}{3} \int \frac {e^{-x^2+x^4}}{8+2 x} \, dx-\frac {5 \operatorname {Subst}\left (\int e^{\frac {1}{4} (-1+2 x)^2} \, dx,x,x^2\right )}{\sqrt [4]{e}}-\frac {35 \operatorname {Subst}\left (\int e^{\frac {1}{4} (-1+2 x)^2} \, dx,x,x^2\right )}{\sqrt [4]{e}}-\frac {170 \operatorname {Subst}\left (\int e^{\frac {1}{4} (-1+2 x)^2} \, dx,x,x^2\right )}{\sqrt [4]{e}}+\frac {210 \operatorname {Subst}\left (\int e^{\frac {1}{4} (-1+2 x)^2} \, dx,x,x^2\right )}{\sqrt [4]{e}}\\ &=6 e^{-x^2+x^4} \log \left (x \left (4+5 x+x^2\right )\right )+2 \int \frac {e^{-x^2+x^4}}{4+x} \, dx+\frac {8}{3} \int \frac {e^{-x^2+x^4}}{2+2 x} \, dx+4 \int e^{-x^2+x^4} x^4 \, dx-\frac {14}{3} \int \frac {e^{-x^2+x^4}}{2+2 x} \, dx-6 \int \frac {e^{-x^2+x^4}}{1+x} \, dx-6 \int \frac {e^{-x^2+x^4}}{4+x} \, dx+\frac {20}{3} \int \frac {e^{-x^2+x^4}}{2+2 x} \, dx-7 \int e^{-x^2+x^4} \, dx-8 \int \frac {e^{-x^2+x^4}}{1+x} \, dx+\frac {28}{3} \int \frac {e^{-x^2+x^4}}{2+2 x} \, dx-\frac {40}{3} \int \frac {e^{-x^2+x^4}}{2+2 x} \, dx+14 \int e^{-x^2+x^4} x^2 \, dx-\frac {46}{3} \int \frac {e^{-x^2+x^4}}{2+2 x} \, dx-\frac {128}{3} \int \frac {e^{-x^2+x^4}}{-2-2 x} \, dx-\frac {128}{3} \int \frac {e^{-x^2+x^4}}{8+2 x} \, dx+50 \int e^{-x^2+x^4} \, dx+\frac {184}{3} \int \frac {e^{-x^2+x^4}}{8+2 x} \, dx+\frac {224}{3} \int \frac {e^{-x^2+x^4}}{8+2 x} \, dx+84 \int e^{-x^2+x^4} x^2 \, dx-100 \int e^{-x^2+x^4} x^2 \, dx+294 \int e^{-x^2+x^4} \, dx-\frac {1280}{3} \int \frac {e^{-x^2+x^4}}{8+2 x} \, dx+1364 \int e^{-x^2+x^4} \, dx-1700 \int e^{-x^2+x^4} \, dx-\frac {7168}{3} \int \frac {e^{-x^2+x^4}}{8+2 x} \, dx-\frac {32768}{3} \int \frac {e^{-x^2+x^4}}{8+2 x} \, dx+\frac {40960}{3} \int \frac {e^{-x^2+x^4}}{8+2 x} \, dx\\ \end {aligned} \end {gather*}

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Mathematica [A]  time = 0.06, size = 27, normalized size = 1.04 \begin {gather*} e^{-x^2+x^4} \left (x+6 \log \left (x \left (4+5 x+x^2\right )\right )\right ) \end {gather*}

Antiderivative was successfully verified.

[In]

Integrate[(E^(-x^2 + x^4)*(x + 6*Log[4*x + 5*x^2 + x^3])*(24 + 64*x + 23*x^2 - 7*x^3 - 10*x^4 + 14*x^5 + 20*x^
6 + 4*x^7 + (-48*x^2 - 60*x^3 + 84*x^4 + 120*x^5 + 24*x^6)*Log[4*x + 5*x^2 + x^3]))/(4*x^2 + 5*x^3 + x^4 + (24
*x + 30*x^2 + 6*x^3)*Log[4*x + 5*x^2 + x^3]),x]

[Out]

E^(-x^2 + x^4)*(x + 6*Log[x*(4 + 5*x + x^2)])

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fricas [A]  time = 0.63, size = 28, normalized size = 1.08 \begin {gather*} e^{\left (x^{4} - x^{2} + \log \left (x + 6 \, \log \left (x^{3} + 5 \, x^{2} + 4 \, x\right )\right )\right )} \end {gather*}

Verification of antiderivative is not currently implemented for this CAS.

[In]

integrate(((24*x^6+120*x^5+84*x^4-60*x^3-48*x^2)*log(x^3+5*x^2+4*x)+4*x^7+20*x^6+14*x^5-10*x^4-7*x^3+23*x^2+64
*x+24)*exp(log(6*log(x^3+5*x^2+4*x)+x)+x^4-x^2)/((6*x^3+30*x^2+24*x)*log(x^3+5*x^2+4*x)+x^4+5*x^3+4*x^2),x, al
gorithm="fricas")

[Out]

e^(x^4 - x^2 + log(x + 6*log(x^3 + 5*x^2 + 4*x)))

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giac [A]  time = 0.91, size = 28, normalized size = 1.08 \begin {gather*} e^{\left (x^{4} - x^{2} + \log \left (x + 6 \, \log \left (x^{3} + 5 \, x^{2} + 4 \, x\right )\right )\right )} \end {gather*}

Verification of antiderivative is not currently implemented for this CAS.

[In]

integrate(((24*x^6+120*x^5+84*x^4-60*x^3-48*x^2)*log(x^3+5*x^2+4*x)+4*x^7+20*x^6+14*x^5-10*x^4-7*x^3+23*x^2+64
*x+24)*exp(log(6*log(x^3+5*x^2+4*x)+x)+x^4-x^2)/((6*x^3+30*x^2+24*x)*log(x^3+5*x^2+4*x)+x^4+5*x^3+4*x^2),x, al
gorithm="giac")

[Out]

e^(x^4 - x^2 + log(x + 6*log(x^3 + 5*x^2 + 4*x)))

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maple [F]  time = 0.07, size = 0, normalized size = 0.00 \[\int \frac {\left (\left (24 x^{6}+120 x^{5}+84 x^{4}-60 x^{3}-48 x^{2}\right ) \ln \left (x^{3}+5 x^{2}+4 x \right )+4 x^{7}+20 x^{6}+14 x^{5}-10 x^{4}-7 x^{3}+23 x^{2}+64 x +24\right ) {\mathrm e}^{\ln \left (6 \ln \left (x^{3}+5 x^{2}+4 x \right )+x \right )+x^{4}-x^{2}}}{\left (6 x^{3}+30 x^{2}+24 x \right ) \ln \left (x^{3}+5 x^{2}+4 x \right )+x^{4}+5 x^{3}+4 x^{2}}\, dx\]

Verification of antiderivative is not currently implemented for this CAS.

[In]

int(((24*x^6+120*x^5+84*x^4-60*x^3-48*x^2)*ln(x^3+5*x^2+4*x)+4*x^7+20*x^6+14*x^5-10*x^4-7*x^3+23*x^2+64*x+24)*
exp(ln(6*ln(x^3+5*x^2+4*x)+x)+x^4-x^2)/((6*x^3+30*x^2+24*x)*ln(x^3+5*x^2+4*x)+x^4+5*x^3+4*x^2),x)

[Out]

int(((24*x^6+120*x^5+84*x^4-60*x^3-48*x^2)*ln(x^3+5*x^2+4*x)+4*x^7+20*x^6+14*x^5-10*x^4-7*x^3+23*x^2+64*x+24)*
exp(ln(6*ln(x^3+5*x^2+4*x)+x)+x^4-x^2)/((6*x^3+30*x^2+24*x)*ln(x^3+5*x^2+4*x)+x^4+5*x^3+4*x^2),x)

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maxima [A]  time = 0.42, size = 29, normalized size = 1.12 \begin {gather*} {\left (x + 6 \, \log \left (x + 4\right ) + 6 \, \log \left (x + 1\right ) + 6 \, \log \relax (x)\right )} e^{\left (x^{4} - x^{2}\right )} \end {gather*}

Verification of antiderivative is not currently implemented for this CAS.

[In]

integrate(((24*x^6+120*x^5+84*x^4-60*x^3-48*x^2)*log(x^3+5*x^2+4*x)+4*x^7+20*x^6+14*x^5-10*x^4-7*x^3+23*x^2+64
*x+24)*exp(log(6*log(x^3+5*x^2+4*x)+x)+x^4-x^2)/((6*x^3+30*x^2+24*x)*log(x^3+5*x^2+4*x)+x^4+5*x^3+4*x^2),x, al
gorithm="maxima")

[Out]

(x + 6*log(x + 4) + 6*log(x + 1) + 6*log(x))*e^(x^4 - x^2)

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mupad [F]  time = 0.00, size = -1, normalized size = -0.04 \begin {gather*} \int \frac {{\mathrm {e}}^{\ln \left (x+6\,\ln \left (x^3+5\,x^2+4\,x\right )\right )-x^2+x^4}\,\left (64\,x+\ln \left (x^3+5\,x^2+4\,x\right )\,\left (24\,x^6+120\,x^5+84\,x^4-60\,x^3-48\,x^2\right )+23\,x^2-7\,x^3-10\,x^4+14\,x^5+20\,x^6+4\,x^7+24\right )}{\ln \left (x^3+5\,x^2+4\,x\right )\,\left (6\,x^3+30\,x^2+24\,x\right )+4\,x^2+5\,x^3+x^4} \,d x \end {gather*}

Verification of antiderivative is not currently implemented for this CAS.

[In]

int((exp(log(x + 6*log(4*x + 5*x^2 + x^3)) - x^2 + x^4)*(64*x + log(4*x + 5*x^2 + x^3)*(84*x^4 - 60*x^3 - 48*x
^2 + 120*x^5 + 24*x^6) + 23*x^2 - 7*x^3 - 10*x^4 + 14*x^5 + 20*x^6 + 4*x^7 + 24))/(log(4*x + 5*x^2 + x^3)*(24*
x + 30*x^2 + 6*x^3) + 4*x^2 + 5*x^3 + x^4),x)

[Out]

int((exp(log(x + 6*log(4*x + 5*x^2 + x^3)) - x^2 + x^4)*(64*x + log(4*x + 5*x^2 + x^3)*(84*x^4 - 60*x^3 - 48*x
^2 + 120*x^5 + 24*x^6) + 23*x^2 - 7*x^3 - 10*x^4 + 14*x^5 + 20*x^6 + 4*x^7 + 24))/(log(4*x + 5*x^2 + x^3)*(24*
x + 30*x^2 + 6*x^3) + 4*x^2 + 5*x^3 + x^4), x)

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sympy [A]  time = 0.62, size = 24, normalized size = 0.92 \begin {gather*} \left (x + 6 \log {\left (x^{3} + 5 x^{2} + 4 x \right )}\right ) e^{x^{4} - x^{2}} \end {gather*}

Verification of antiderivative is not currently implemented for this CAS.

[In]

integrate(((24*x**6+120*x**5+84*x**4-60*x**3-48*x**2)*ln(x**3+5*x**2+4*x)+4*x**7+20*x**6+14*x**5-10*x**4-7*x**
3+23*x**2+64*x+24)*exp(ln(6*ln(x**3+5*x**2+4*x)+x)+x**4-x**2)/((6*x**3+30*x**2+24*x)*ln(x**3+5*x**2+4*x)+x**4+
5*x**3+4*x**2),x)

[Out]

(x + 6*log(x**3 + 5*x**2 + 4*x))*exp(x**4 - x**2)

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