\(\int (e^{5 x^3} (32-1920 x^2+480 x^3)+e^{10 x^3} (-128+32 x+7680 x^2-3840 x^3+480 x^4)+(64 x+e^{5 x^3} (-256 x+64 x^2)) \log (x)+(64 x+e^{5 x^3} (-256 x+96 x^2-1920 x^4+480 x^5)) \log ^2(x)+64 x^3 \log ^3(x)+64 x^3 \log ^4(x)) \, dx\) [6961]

Optimal result

Integrand size = 127, antiderivative size = 25 \[ \int \left (e^{5 x^3} \left (32-1920 x^2+480 x^3\right )+e^{10 x^3} \left (-128+32 x+7680 x^2-3840 x^3+480 x^4\right )+\left (64 x+e^{5 x^3} \left (-256 x+64 x^2\right )\right ) \log (x)+\left (64 x+e^{5 x^3} \left (-256 x+96 x^2-1920 x^4+480 x^5\right )\right ) \log ^2(x)+64 x^3 \log ^3(x)+64 x^3 \log ^4(x)\right ) \, dx=16 \left (1+e^{5 x^3} (-4+x)+x^2 \log ^2(x)\right )^2 \]

[Out]

16*(1+(x-4)*exp(5*x^3)+x^2*ln(x)^2)^2

Rubi [F]

\[ \int \left (e^{5 x^3} \left (32-1920 x^2+480 x^3\right )+e^{10 x^3} \left (-128+32 x+7680 x^2-3840 x^3+480 x^4\right )+\left (64 x+e^{5 x^3} \left (-256 x+64 x^2\right )\right ) \log (x)+\left (64 x+e^{5 x^3} \left (-256 x+96 x^2-1920 x^4+480 x^5\right )\right ) \log ^2(x)+64 x^3 \log ^3(x)+64 x^3 \log ^4(x)\right ) \, dx=\int \left (e^{5 x^3} \left (32-1920 x^2+480 x^3\right )+e^{10 x^3} \left (-128+32 x+7680 x^2-3840 x^3+480 x^4\right )+\left (64 x+e^{5 x^3} \left (-256 x+64 x^2\right )\right ) \log (x)+\left (64 x+e^{5 x^3} \left (-256 x+96 x^2-1920 x^4+480 x^5\right )\right ) \log ^2(x)+64 x^3 \log ^3(x)+64 x^3 \log ^4(x)\right ) \, dx \]

[In]

Int[E^(5*x^3)*(32 - 1920*x^2 + 480*x^3) + E^(10*x^3)*(-128 + 32*x + 7680*x^2 - 3840*x^3 + 480*x^4) + (64*x + E
^(5*x^3)*(-256*x + 64*x^2))*Log[x] + (64*x + E^(5*x^3)*(-256*x + 96*x^2 - 1920*x^4 + 480*x^5))*Log[x]^2 + 64*x
^3*Log[x]^3 + 64*x^3*Log[x]^4,x]

[Out]

-128*E^(5*x^3) + 256*E^(10*x^3) - (64*ExpIntegralEi[5*x^3])/45 + (64*2^(2/3)*x*Gamma[1/3, -10*x^3])/(3*5^(1/3)
*(-x^3)^(1/3)) - (32*x*Gamma[1/3, -5*x^3])/(3*5^(1/3)*(-x^3)^(1/3)) - (16*2^(1/3)*x^2*Gamma[2/3, -10*x^3])/(3*
5^(2/3)*(-x^3)^(2/3)) + (64*2^(2/3)*x^4*Gamma[4/3, -10*x^3])/(5^(1/3)*(-x^3)^(4/3)) - (32*x^4*Gamma[4/3, -5*x^
3])/(5^(1/3)*(-x^3)^(4/3)) - (8*2^(1/3)*x^5*Gamma[5/3, -10*x^3])/(5^(2/3)*(-x^3)^(5/3)) + 64*x^2*Hypergeometri
cPFQ[{2/3, 2/3}, {5/3, 5/3}, 5*x^3] + (64*E^(5*x^3)*Log[x])/15 - (256*x^2*Gamma[2/3]*Log[x])/(3*5^(2/3)*(-x^3)
^(2/3)) + (256*x^2*Gamma[2/3, -5*x^3]*Log[x])/(3*5^(2/3)*(-x^3)^(2/3)) + 32*x^2*Log[x]^2 + 16*x^4*Log[x]^4 - 2
56*Defer[Int][E^(5*x^3)*x*Log[x]^2, x] + 96*Defer[Int][E^(5*x^3)*x^2*Log[x]^2, x] - 1920*Defer[Int][E^(5*x^3)*
x^4*Log[x]^2, x] + 480*Defer[Int][E^(5*x^3)*x^5*Log[x]^2, x]

Rubi steps \begin{align*} \text {integral}& = 64 \int x^3 \log ^3(x) \, dx+64 \int x^3 \log ^4(x) \, dx+\int e^{5 x^3} \left (32-1920 x^2+480 x^3\right ) \, dx+\int e^{10 x^3} \left (-128+32 x+7680 x^2-3840 x^3+480 x^4\right ) \, dx+\int \left (64 x+e^{5 x^3} \left (-256 x+64 x^2\right )\right ) \log (x) \, dx+\int \left (64 x+e^{5 x^3} \left (-256 x+96 x^2-1920 x^4+480 x^5\right )\right ) \log ^2(x) \, dx \\ & = \frac {64}{15} e^{5 x^3} \log (x)+32 x^2 \log (x)+\frac {256 x^2 \Gamma \left (\frac {2}{3},-5 x^3\right ) \log (x)}{3\ 5^{2/3} \left (-x^3\right )^{2/3}}+16 x^4 \log ^3(x)+16 x^4 \log ^4(x)-48 \int x^3 \log ^2(x) \, dx-64 \int x^3 \log ^3(x) \, dx+\int \left (32 e^{5 x^3}-1920 e^{5 x^3} x^2+480 e^{5 x^3} x^3\right ) \, dx+\int \left (-128 e^{10 x^3}+32 e^{10 x^3} x+7680 e^{10 x^3} x^2-3840 e^{10 x^3} x^3+480 e^{10 x^3} x^4\right ) \, dx-\int \frac {32 \left (2 e^{5 x^3} x+15 x^3-8 \sqrt [3]{5} \sqrt [3]{-x^3} \Gamma \left (\frac {2}{3},-5 x^3\right )\right )}{15 x^2} \, dx+\int \left (64 x \log ^2(x)+32 e^{5 x^3} x \left (-8+3 x-60 x^3+15 x^4\right ) \log ^2(x)\right ) \, dx \\ & = \frac {64}{15} e^{5 x^3} \log (x)+32 x^2 \log (x)+\frac {256 x^2 \Gamma \left (\frac {2}{3},-5 x^3\right ) \log (x)}{3\ 5^{2/3} \left (-x^3\right )^{2/3}}-12 x^4 \log ^2(x)+16 x^4 \log ^4(x)-\frac {32}{15} \int \frac {2 e^{5 x^3} x+15 x^3-8 \sqrt [3]{5} \sqrt [3]{-x^3} \Gamma \left (\frac {2}{3},-5 x^3\right )}{x^2} \, dx+24 \int x^3 \log (x) \, dx+32 \int e^{5 x^3} \, dx+32 \int e^{10 x^3} x \, dx+32 \int e^{5 x^3} x \left (-8+3 x-60 x^3+15 x^4\right ) \log ^2(x) \, dx+48 \int x^3 \log ^2(x) \, dx+64 \int x \log ^2(x) \, dx-128 \int e^{10 x^3} \, dx+480 \int e^{5 x^3} x^3 \, dx+480 \int e^{10 x^3} x^4 \, dx-1920 \int e^{5 x^3} x^2 \, dx-3840 \int e^{10 x^3} x^3 \, dx+7680 \int e^{10 x^3} x^2 \, dx \\ & = -128 e^{5 x^3}+256 e^{10 x^3}-\frac {3 x^4}{2}+\frac {64\ 2^{2/3} x \Gamma \left (\frac {1}{3},-10 x^3\right )}{3 \sqrt [3]{5} \sqrt [3]{-x^3}}-\frac {32 x \Gamma \left (\frac {1}{3},-5 x^3\right )}{3 \sqrt [3]{5} \sqrt [3]{-x^3}}-\frac {16 \sqrt [3]{2} x^2 \Gamma \left (\frac {2}{3},-10 x^3\right )}{3\ 5^{2/3} \left (-x^3\right )^{2/3}}+\frac {64\ 2^{2/3} x^4 \Gamma \left (\frac {4}{3},-10 x^3\right )}{\sqrt [3]{5} \left (-x^3\right )^{4/3}}-\frac {32 x^4 \Gamma \left (\frac {4}{3},-5 x^3\right )}{\sqrt [3]{5} \left (-x^3\right )^{4/3}}-\frac {8 \sqrt [3]{2} x^5 \Gamma \left (\frac {5}{3},-10 x^3\right )}{5^{2/3} \left (-x^3\right )^{5/3}}+\frac {64}{15} e^{5 x^3} \log (x)+32 x^2 \log (x)+6 x^4 \log (x)+\frac {256 x^2 \Gamma \left (\frac {2}{3},-5 x^3\right ) \log (x)}{3\ 5^{2/3} \left (-x^3\right )^{2/3}}+32 x^2 \log ^2(x)+16 x^4 \log ^4(x)-\frac {32}{15} \int \left (\frac {2 e^{5 x^3}}{x}+15 x+\frac {8 \sqrt [3]{5} x \Gamma \left (\frac {2}{3},-5 x^3\right )}{\left (-x^3\right )^{2/3}}\right ) \, dx-24 \int x^3 \log (x) \, dx+32 \int \left (-8 e^{5 x^3} x \log ^2(x)+3 e^{5 x^3} x^2 \log ^2(x)-60 e^{5 x^3} x^4 \log ^2(x)+15 e^{5 x^3} x^5 \log ^2(x)\right ) \, dx-64 \int x \log (x) \, dx \\ & = -128 e^{5 x^3}+256 e^{10 x^3}+\frac {64\ 2^{2/3} x \Gamma \left (\frac {1}{3},-10 x^3\right )}{3 \sqrt [3]{5} \sqrt [3]{-x^3}}-\frac {32 x \Gamma \left (\frac {1}{3},-5 x^3\right )}{3 \sqrt [3]{5} \sqrt [3]{-x^3}}-\frac {16 \sqrt [3]{2} x^2 \Gamma \left (\frac {2}{3},-10 x^3\right )}{3\ 5^{2/3} \left (-x^3\right )^{2/3}}+\frac {64\ 2^{2/3} x^4 \Gamma \left (\frac {4}{3},-10 x^3\right )}{\sqrt [3]{5} \left (-x^3\right )^{4/3}}-\frac {32 x^4 \Gamma \left (\frac {4}{3},-5 x^3\right )}{\sqrt [3]{5} \left (-x^3\right )^{4/3}}-\frac {8 \sqrt [3]{2} x^5 \Gamma \left (\frac {5}{3},-10 x^3\right )}{5^{2/3} \left (-x^3\right )^{5/3}}+\frac {64}{15} e^{5 x^3} \log (x)+\frac {256 x^2 \Gamma \left (\frac {2}{3},-5 x^3\right ) \log (x)}{3\ 5^{2/3} \left (-x^3\right )^{2/3}}+32 x^2 \log ^2(x)+16 x^4 \log ^4(x)-\frac {64}{15} \int \frac {e^{5 x^3}}{x} \, dx+96 \int e^{5 x^3} x^2 \log ^2(x) \, dx-256 \int e^{5 x^3} x \log ^2(x) \, dx+480 \int e^{5 x^3} x^5 \log ^2(x) \, dx-1920 \int e^{5 x^3} x^4 \log ^2(x) \, dx-\frac {256 \int \frac {x \Gamma \left (\frac {2}{3},-5 x^3\right )}{\left (-x^3\right )^{2/3}} \, dx}{3\ 5^{2/3}} \\ & = -128 e^{5 x^3}+256 e^{10 x^3}-\frac {64 \text {Ei}\left (5 x^3\right )}{45}+\frac {64\ 2^{2/3} x \Gamma \left (\frac {1}{3},-10 x^3\right )}{3 \sqrt [3]{5} \sqrt [3]{-x^3}}-\frac {32 x \Gamma \left (\frac {1}{3},-5 x^3\right )}{3 \sqrt [3]{5} \sqrt [3]{-x^3}}-\frac {16 \sqrt [3]{2} x^2 \Gamma \left (\frac {2}{3},-10 x^3\right )}{3\ 5^{2/3} \left (-x^3\right )^{2/3}}+\frac {64\ 2^{2/3} x^4 \Gamma \left (\frac {4}{3},-10 x^3\right )}{\sqrt [3]{5} \left (-x^3\right )^{4/3}}-\frac {32 x^4 \Gamma \left (\frac {4}{3},-5 x^3\right )}{\sqrt [3]{5} \left (-x^3\right )^{4/3}}-\frac {8 \sqrt [3]{2} x^5 \Gamma \left (\frac {5}{3},-10 x^3\right )}{5^{2/3} \left (-x^3\right )^{5/3}}+\frac {64}{15} e^{5 x^3} \log (x)+\frac {256 x^2 \Gamma \left (\frac {2}{3},-5 x^3\right ) \log (x)}{3\ 5^{2/3} \left (-x^3\right )^{2/3}}+32 x^2 \log ^2(x)+16 x^4 \log ^4(x)+96 \int e^{5 x^3} x^2 \log ^2(x) \, dx-256 \int e^{5 x^3} x \log ^2(x) \, dx+480 \int e^{5 x^3} x^5 \log ^2(x) \, dx-1920 \int e^{5 x^3} x^4 \log ^2(x) \, dx-\frac {\left (256 x^2\right ) \int \frac {\Gamma \left (\frac {2}{3},-5 x^3\right )}{x} \, dx}{3\ 5^{2/3} \left (-x^3\right )^{2/3}} \\ & = -128 e^{5 x^3}+256 e^{10 x^3}-\frac {64 \text {Ei}\left (5 x^3\right )}{45}+\frac {64\ 2^{2/3} x \Gamma \left (\frac {1}{3},-10 x^3\right )}{3 \sqrt [3]{5} \sqrt [3]{-x^3}}-\frac {32 x \Gamma \left (\frac {1}{3},-5 x^3\right )}{3 \sqrt [3]{5} \sqrt [3]{-x^3}}-\frac {16 \sqrt [3]{2} x^2 \Gamma \left (\frac {2}{3},-10 x^3\right )}{3\ 5^{2/3} \left (-x^3\right )^{2/3}}+\frac {64\ 2^{2/3} x^4 \Gamma \left (\frac {4}{3},-10 x^3\right )}{\sqrt [3]{5} \left (-x^3\right )^{4/3}}-\frac {32 x^4 \Gamma \left (\frac {4}{3},-5 x^3\right )}{\sqrt [3]{5} \left (-x^3\right )^{4/3}}-\frac {8 \sqrt [3]{2} x^5 \Gamma \left (\frac {5}{3},-10 x^3\right )}{5^{2/3} \left (-x^3\right )^{5/3}}+\frac {64}{15} e^{5 x^3} \log (x)+\frac {256 x^2 \Gamma \left (\frac {2}{3},-5 x^3\right ) \log (x)}{3\ 5^{2/3} \left (-x^3\right )^{2/3}}+32 x^2 \log ^2(x)+16 x^4 \log ^4(x)+96 \int e^{5 x^3} x^2 \log ^2(x) \, dx-256 \int e^{5 x^3} x \log ^2(x) \, dx+480 \int e^{5 x^3} x^5 \log ^2(x) \, dx-1920 \int e^{5 x^3} x^4 \log ^2(x) \, dx-\frac {\left (256 x^2\right ) \text {Subst}\left (\int \frac {\Gamma \left (\frac {2}{3},-5 x\right )}{x} \, dx,x,x^3\right )}{9\ 5^{2/3} \left (-x^3\right )^{2/3}} \\ & = -128 e^{5 x^3}+256 e^{10 x^3}-\frac {64 \text {Ei}\left (5 x^3\right )}{45}+\frac {64\ 2^{2/3} x \Gamma \left (\frac {1}{3},-10 x^3\right )}{3 \sqrt [3]{5} \sqrt [3]{-x^3}}-\frac {32 x \Gamma \left (\frac {1}{3},-5 x^3\right )}{3 \sqrt [3]{5} \sqrt [3]{-x^3}}-\frac {16 \sqrt [3]{2} x^2 \Gamma \left (\frac {2}{3},-10 x^3\right )}{3\ 5^{2/3} \left (-x^3\right )^{2/3}}+\frac {64\ 2^{2/3} x^4 \Gamma \left (\frac {4}{3},-10 x^3\right )}{\sqrt [3]{5} \left (-x^3\right )^{4/3}}-\frac {32 x^4 \Gamma \left (\frac {4}{3},-5 x^3\right )}{\sqrt [3]{5} \left (-x^3\right )^{4/3}}-\frac {8 \sqrt [3]{2} x^5 \Gamma \left (\frac {5}{3},-10 x^3\right )}{5^{2/3} \left (-x^3\right )^{5/3}}+64 x^2 \, _2F_2\left (\frac {2}{3},\frac {2}{3};\frac {5}{3},\frac {5}{3};5 x^3\right )+\frac {64}{15} e^{5 x^3} \log (x)-\frac {256 x^2 \Gamma \left (\frac {2}{3}\right ) \log (x)}{3\ 5^{2/3} \left (-x^3\right )^{2/3}}+\frac {256 x^2 \Gamma \left (\frac {2}{3},-5 x^3\right ) \log (x)}{3\ 5^{2/3} \left (-x^3\right )^{2/3}}+32 x^2 \log ^2(x)+16 x^4 \log ^4(x)+96 \int e^{5 x^3} x^2 \log ^2(x) \, dx-256 \int e^{5 x^3} x \log ^2(x) \, dx+480 \int e^{5 x^3} x^5 \log ^2(x) \, dx-1920 \int e^{5 x^3} x^4 \log ^2(x) \, dx \\ \end{align*}

Mathematica [C] (verified)

Result contains higher order function than in optimal. Order 5 vs. order 3 in optimal.

Time = 0.78 (sec) , antiderivative size = 316, normalized size of antiderivative = 12.64 \[ \int \left (e^{5 x^3} \left (32-1920 x^2+480 x^3\right )+e^{10 x^3} \left (-128+32 x+7680 x^2-3840 x^3+480 x^4\right )+\left (64 x+e^{5 x^3} \left (-256 x+64 x^2\right )\right ) \log (x)+\left (64 x+e^{5 x^3} \left (-256 x+96 x^2-1920 x^4+480 x^5\right )\right ) \log ^2(x)+64 x^3 \log ^3(x)+64 x^3 \log ^4(x)\right ) \, dx=32 \left (\frac {1}{2}-4 e^{5 x^3}+8 e^{10 x^3}+e^{5 x^3} x-4 e^{10 x^3} x+\frac {1}{2} e^{10 x^3} x^2-2 x^2 \, _3F_3\left (\frac {2}{3},\frac {2}{3},\frac {2}{3};\frac {5}{3},\frac {5}{3},\frac {5}{3};5 x^3\right )-\frac {24}{25} x^5 \, _3F_3\left (\frac {5}{3},\frac {5}{3},\frac {5}{3};\frac {8}{3},\frac {8}{3},\frac {8}{3};5 x^3\right )+\frac {8 \sqrt [3]{-x^3} \Gamma \left (\frac {2}{3},0,-5 x^3\right ) \log (x)}{3\ 5^{2/3} x}+\frac {24}{5} x^5 \, _2F_2\left (\frac {5}{3},\frac {5}{3};\frac {8}{3},\frac {8}{3};5 x^3\right ) \log (x)+x^2 \log ^2(x)+e^{5 x^3} x^3 \log ^2(x)+\frac {8 \sqrt [3]{-x^3} \Gamma \left (\frac {2}{3},0,-5 x^3\right ) \log ^2(x)}{3\ 5^{2/3} x}+\frac {4 x^2 \Gamma \left (\frac {5}{3},0,-5 x^3\right ) \log ^2(x)}{5^{2/3} \left (-x^3\right )^{2/3}}+\frac {1}{2} x^4 \log ^4(x)+2 x^2 \, _2F_2\left (\frac {2}{3},\frac {2}{3};\frac {5}{3},\frac {5}{3};5 x^3\right ) (1+2 \log (x))\right ) \]

[In]

Integrate[E^(5*x^3)*(32 - 1920*x^2 + 480*x^3) + E^(10*x^3)*(-128 + 32*x + 7680*x^2 - 3840*x^3 + 480*x^4) + (64
*x + E^(5*x^3)*(-256*x + 64*x^2))*Log[x] + (64*x + E^(5*x^3)*(-256*x + 96*x^2 - 1920*x^4 + 480*x^5))*Log[x]^2
+ 64*x^3*Log[x]^3 + 64*x^3*Log[x]^4,x]

[Out]

32*(1/2 - 4*E^(5*x^3) + 8*E^(10*x^3) + E^(5*x^3)*x - 4*E^(10*x^3)*x + (E^(10*x^3)*x^2)/2 - 2*x^2*Hypergeometri
cPFQ[{2/3, 2/3, 2/3}, {5/3, 5/3, 5/3}, 5*x^3] - (24*x^5*HypergeometricPFQ[{5/3, 5/3, 5/3}, {8/3, 8/3, 8/3}, 5*
x^3])/25 + (8*(-x^3)^(1/3)*Gamma[2/3, 0, -5*x^3]*Log[x])/(3*5^(2/3)*x) + (24*x^5*HypergeometricPFQ[{5/3, 5/3},
{8/3, 8/3}, 5*x^3]*Log[x])/5 + x^2*Log[x]^2 + E^(5*x^3)*x^3*Log[x]^2 + (8*(-x^3)^(1/3)*Gamma[2/3, 0, -5*x^3]*
Log[x]^2)/(3*5^(2/3)*x) + (4*x^2*Gamma[5/3, 0, -5*x^3]*Log[x]^2)/(5^(2/3)*(-x^3)^(2/3)) + (x^4*Log[x]^4)/2 + 2
*x^2*HypergeometricPFQ[{2/3, 2/3}, {5/3, 5/3}, 5*x^3]*(1 + 2*Log[x]))

Maple [B] (verified)

Leaf count of result is larger than twice the leaf count of optimal. \(74\) vs. \(2(24)=48\).

Time = 0.21 (sec) , antiderivative size = 75, normalized size of antiderivative = 3.00

method	result	size
risch	\(16 x^{4} \ln \left (x \right )^{4}+\left (16 x^{2}-128 x +256\right ) {\mathrm e}^{10 x^{3}}+\left (32 x -128\right ) {\mathrm e}^{5 x^{3}}+\left (32 \,{\mathrm e}^{5 x^{3}} x^{3}-128 x^{2} {\mathrm e}^{5 x^{3}}+32 x^{2}\right ) \ln \left (x \right )^{2}\)	\(75\)
parallelrisch	\(16 x^{4} \ln \left (x \right )^{4}+32 \,{\mathrm e}^{5 x^{3}} \ln \left (x \right )^{2} x^{3}-128 \,{\mathrm e}^{5 x^{3}} \ln \left (x \right )^{2} x^{2}+32 x^{2} \ln \left (x \right )^{2}+16 \,{\mathrm e}^{10 x^{3}} x^{2}+32 \,{\mathrm e}^{5 x^{3}} x -128 \,{\mathrm e}^{10 x^{3}} x -128 \,{\mathrm e}^{5 x^{3}}+256 \,{\mathrm e}^{10 x^{3}}\)	\(101\)

[In]

int(64*x^3*ln(x)^4+64*x^3*ln(x)^3+((480*x^5-1920*x^4+96*x^2-256*x)*exp(5*x^3)+64*x)*ln(x)^2+((64*x^2-256*x)*ex
p(5*x^3)+64*x)*ln(x)+(480*x^4-3840*x^3+7680*x^2+32*x-128)*exp(5*x^3)^2+(480*x^3-1920*x^2+32)*exp(5*x^3),x,meth
od=_RETURNVERBOSE)

[Out]

16*x^4*ln(x)^4+(16*x^2-128*x+256)*exp(5*x^3)^2+(32*x-128)*exp(5*x^3)+(32*exp(5*x^3)*x^3-128*x^2*exp(5*x^3)+32*
x^2)*ln(x)^2

Fricas [B] (verification not implemented)

Leaf count of result is larger than twice the leaf count of optimal. 63 vs. \(2 (24) = 48\).

Time = 0.23 (sec) , antiderivative size = 63, normalized size of antiderivative = 2.52 \[ \int \left (e^{5 x^3} \left (32-1920 x^2+480 x^3\right )+e^{10 x^3} \left (-128+32 x+7680 x^2-3840 x^3+480 x^4\right )+\left (64 x+e^{5 x^3} \left (-256 x+64 x^2\right )\right ) \log (x)+\left (64 x+e^{5 x^3} \left (-256 x+96 x^2-1920 x^4+480 x^5\right )\right ) \log ^2(x)+64 x^3 \log ^3(x)+64 x^3 \log ^4(x)\right ) \, dx=16 \, x^{4} \log \left (x\right )^{4} + 32 \, {\left (x^{2} + {\left (x^{3} - 4 \, x^{2}\right )} e^{\left (5 \, x^{3}\right )}\right )} \log \left (x\right )^{2} + 16 \, {\left (x^{2} - 8 \, x + 16\right )} e^{\left (10 \, x^{3}\right )} + 32 \, {\left (x - 4\right )} e^{\left (5 \, x^{3}\right )} \]

[In]

integrate(64*x^3*log(x)^4+64*x^3*log(x)^3+((480*x^5-1920*x^4+96*x^2-256*x)*exp(5*x^3)+64*x)*log(x)^2+((64*x^2-
256*x)*exp(5*x^3)+64*x)*log(x)+(480*x^4-3840*x^3+7680*x^2+32*x-128)*exp(5*x^3)^2+(480*x^3-1920*x^2+32)*exp(5*x
^3),x, algorithm="fricas")

[Out]

16*x^4*log(x)^4 + 32*(x^2 + (x^3 - 4*x^2)*e^(5*x^3))*log(x)^2 + 16*(x^2 - 8*x + 16)*e^(10*x^3) + 32*(x - 4)*e^
(5*x^3)

Sympy [B] (verification not implemented)

Leaf count of result is larger than twice the leaf count of optimal. 68 vs. \(2 (22) = 44\).

Time = 0.21 (sec) , antiderivative size = 68, normalized size of antiderivative = 2.72 \[ \int \left (e^{5 x^3} \left (32-1920 x^2+480 x^3\right )+e^{10 x^3} \left (-128+32 x+7680 x^2-3840 x^3+480 x^4\right )+\left (64 x+e^{5 x^3} \left (-256 x+64 x^2\right )\right ) \log (x)+\left (64 x+e^{5 x^3} \left (-256 x+96 x^2-1920 x^4+480 x^5\right )\right ) \log ^2(x)+64 x^3 \log ^3(x)+64 x^3 \log ^4(x)\right ) \, dx=16 x^{4} \log {\left (x \right )}^{4} + 32 x^{2} \log {\left (x \right )}^{2} + \left (16 x^{2} - 128 x + 256\right ) e^{10 x^{3}} + \left (32 x^{3} \log {\left (x \right )}^{2} - 128 x^{2} \log {\left (x \right )}^{2} + 32 x - 128\right ) e^{5 x^{3}} \]

[In]

integrate(64*x**3*ln(x)**4+64*x**3*ln(x)**3+((480*x**5-1920*x**4+96*x**2-256*x)*exp(5*x**3)+64*x)*ln(x)**2+((6
4*x**2-256*x)*exp(5*x**3)+64*x)*ln(x)+(480*x**4-3840*x**3+7680*x**2+32*x-128)*exp(5*x**3)**2+(480*x**3-1920*x*
*2+32)*exp(5*x**3),x)

[Out]

16*x**4*log(x)**4 + 32*x**2*log(x)**2 + (16*x**2 - 128*x + 256)*exp(10*x**3) + (32*x**3*log(x)**2 - 128*x**2*l
og(x)**2 + 32*x - 128)*exp(5*x**3)

Maxima [C] (verification not implemented)

Result contains higher order function than in optimal. Order 4 vs. order 3.

Time = 0.23 (sec) , antiderivative size = 106, normalized size of antiderivative = 4.24 \[ \int \left (e^{5 x^3} \left (32-1920 x^2+480 x^3\right )+e^{10 x^3} \left (-128+32 x+7680 x^2-3840 x^3+480 x^4\right )+\left (64 x+e^{5 x^3} \left (-256 x+64 x^2\right )\right ) \log (x)+\left (64 x+e^{5 x^3} \left (-256 x+96 x^2-1920 x^4+480 x^5\right )\right ) \log ^2(x)+64 x^3 \log ^3(x)+64 x^3 \log ^4(x)\right ) \, dx=16 \, x^{4} \log \left (x\right )^{4} - \frac {32 \cdot 5^{\frac {2}{3}} x^{4} \Gamma \left (\frac {4}{3}, -5 \, x^{3}\right )}{5 \, \left (-x^{3}\right )^{\frac {4}{3}}} + 32 \, x^{2} \log \left (x\right )^{2} + 32 \, {\left (x^{3} - 4 \, x^{2}\right )} e^{\left (5 \, x^{3}\right )} \log \left (x\right )^{2} - \frac {32 \cdot 5^{\frac {2}{3}} x \Gamma \left (\frac {1}{3}, -5 \, x^{3}\right )}{15 \, \left (-x^{3}\right )^{\frac {1}{3}}} + 16 \, {\left (x^{2} - 8 \, x + 16\right )} e^{\left (10 \, x^{3}\right )} - 128 \, e^{\left (5 \, x^{3}\right )} \]

[In]

integrate(64*x^3*log(x)^4+64*x^3*log(x)^3+((480*x^5-1920*x^4+96*x^2-256*x)*exp(5*x^3)+64*x)*log(x)^2+((64*x^2-
256*x)*exp(5*x^3)+64*x)*log(x)+(480*x^4-3840*x^3+7680*x^2+32*x-128)*exp(5*x^3)^2+(480*x^3-1920*x^2+32)*exp(5*x
^3),x, algorithm="maxima")

[Out]

16*x^4*log(x)^4 - 32/5*5^(2/3)*x^4*gamma(4/3, -5*x^3)/(-x^3)^(4/3) + 32*x^2*log(x)^2 + 32*(x^3 - 4*x^2)*e^(5*x
^3)*log(x)^2 - 32/15*5^(2/3)*x*gamma(1/3, -5*x^3)/(-x^3)^(1/3) + 16*(x^2 - 8*x + 16)*e^(10*x^3) - 128*e^(5*x^3
)

Giac [F]

\[ \int \left (e^{5 x^3} \left (32-1920 x^2+480 x^3\right )+e^{10 x^3} \left (-128+32 x+7680 x^2-3840 x^3+480 x^4\right )+\left (64 x+e^{5 x^3} \left (-256 x+64 x^2\right )\right ) \log (x)+\left (64 x+e^{5 x^3} \left (-256 x+96 x^2-1920 x^4+480 x^5\right )\right ) \log ^2(x)+64 x^3 \log ^3(x)+64 x^3 \log ^4(x)\right ) \, dx=\int { 64 \, x^{3} \log \left (x\right )^{4} + 64 \, x^{3} \log \left (x\right )^{3} + 32 \, {\left ({\left (15 \, x^{5} - 60 \, x^{4} + 3 \, x^{2} - 8 \, x\right )} e^{\left (5 \, x^{3}\right )} + 2 \, x\right )} \log \left (x\right )^{2} + 32 \, {\left (15 \, x^{4} - 120 \, x^{3} + 240 \, x^{2} + x - 4\right )} e^{\left (10 \, x^{3}\right )} + 32 \, {\left (15 \, x^{3} - 60 \, x^{2} + 1\right )} e^{\left (5 \, x^{3}\right )} + 64 \, {\left ({\left (x^{2} - 4 \, x\right )} e^{\left (5 \, x^{3}\right )} + x\right )} \log \left (x\right ) \,d x } \]

[In]

integrate(64*x^3*log(x)^4+64*x^3*log(x)^3+((480*x^5-1920*x^4+96*x^2-256*x)*exp(5*x^3)+64*x)*log(x)^2+((64*x^2-
256*x)*exp(5*x^3)+64*x)*log(x)+(480*x^4-3840*x^3+7680*x^2+32*x-128)*exp(5*x^3)^2+(480*x^3-1920*x^2+32)*exp(5*x
^3),x, algorithm="giac")

[Out]

integrate(64*x^3*log(x)^4 + 64*x^3*log(x)^3 + 32*((15*x^5 - 60*x^4 + 3*x^2 - 8*x)*e^(5*x^3) + 2*x)*log(x)^2 +
32*(15*x^4 - 120*x^3 + 240*x^2 + x - 4)*e^(10*x^3) + 32*(15*x^3 - 60*x^2 + 1)*e^(5*x^3) + 64*((x^2 - 4*x)*e^(5
*x^3) + x)*log(x), x)

Mupad [F(-1)]

Timed out. \[ \int \left (e^{5 x^3} \left (32-1920 x^2+480 x^3\right )+e^{10 x^3} \left (-128+32 x+7680 x^2-3840 x^3+480 x^4\right )+\left (64 x+e^{5 x^3} \left (-256 x+64 x^2\right )\right ) \log (x)+\left (64 x+e^{5 x^3} \left (-256 x+96 x^2-1920 x^4+480 x^5\right )\right ) \log ^2(x)+64 x^3 \log ^3(x)+64 x^3 \log ^4(x)\right ) \, dx=\int 64\,x^3\,{\ln \left (x\right )}^3+64\,x^3\,{\ln \left (x\right )}^4+{\ln \left (x\right )}^2\,\left (64\,x-{\mathrm {e}}^{5\,x^3}\,\left (-480\,x^5+1920\,x^4-96\,x^2+256\,x\right )\right )+{\mathrm {e}}^{5\,x^3}\,\left (480\,x^3-1920\,x^2+32\right )+{\mathrm {e}}^{10\,x^3}\,\left (480\,x^4-3840\,x^3+7680\,x^2+32\,x-128\right )+\ln \left (x\right )\,\left (64\,x-{\mathrm {e}}^{5\,x^3}\,\left (256\,x-64\,x^2\right )\right ) \,d x \]

[In]

int(64*x^3*log(x)^3 + 64*x^3*log(x)^4 + log(x)^2*(64*x - exp(5*x^3)*(256*x - 96*x^2 + 1920*x^4 - 480*x^5)) + e
xp(5*x^3)*(480*x^3 - 1920*x^2 + 32) + exp(10*x^3)*(32*x + 7680*x^2 - 3840*x^3 + 480*x^4 - 128) + log(x)*(64*x
- exp(5*x^3)*(256*x - 64*x^2)),x)

[Out]

int(64*x^3*log(x)^3 + 64*x^3*log(x)^4 + log(x)^2*(64*x - exp(5*x^3)*(256*x - 96*x^2 + 1920*x^4 - 480*x^5)) + e
xp(5*x^3)*(480*x^3 - 1920*x^2 + 32) + exp(10*x^3)*(32*x + 7680*x^2 - 3840*x^3 + 480*x^4 - 128) + log(x)*(64*x
- exp(5*x^3)*(256*x - 64*x^2)), x)