3.98.21 \(\int (18 x^2+44 x^3+30 x^4+30 x^5+112 x^6+128 x^7+36 x^8+60 x^9+154 x^{10}+72 x^{11}+56 x^{13}+60 x^{14}+18 x^{17}+2 \log (\log (4))) \, dx\)

Optimal. Leaf size=32 \[ x^2 \left (x+\left (-1-x-x^4\right )^2\right )^2-(x-\log (\log (4)))^2 \]

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Rubi [B]  time = 0.02, antiderivative size = 70, normalized size of antiderivative = 2.19, number of steps used = 1, number of rules used = 0, integrand size = 71, \(\frac {\text {number of rules}}{\text {integrand size}}\) = 0.000, Rules used = {} \begin {gather*} x^{18}+4 x^{15}+4 x^{14}+6 x^{12}+14 x^{11}+6 x^{10}+4 x^9+16 x^8+16 x^7+5 x^6+6 x^5+11 x^4+6 x^3+2 x \log (\log (4)) \end {gather*}

Antiderivative was successfully verified.

[In]

Int[18*x^2 + 44*x^3 + 30*x^4 + 30*x^5 + 112*x^6 + 128*x^7 + 36*x^8 + 60*x^9 + 154*x^10 + 72*x^11 + 56*x^13 + 6
0*x^14 + 18*x^17 + 2*Log[Log[4]],x]

[Out]

6*x^3 + 11*x^4 + 6*x^5 + 5*x^6 + 16*x^7 + 16*x^8 + 4*x^9 + 6*x^10 + 14*x^11 + 6*x^12 + 4*x^14 + 4*x^15 + x^18
+ 2*x*Log[Log[4]]

Rubi steps

\begin {gather*} \begin {aligned} \text {integral} &=6 x^3+11 x^4+6 x^5+5 x^6+16 x^7+16 x^8+4 x^9+6 x^{10}+14 x^{11}+6 x^{12}+4 x^{14}+4 x^{15}+x^{18}+2 x \log (\log (4))\\ \end {aligned} \end {gather*}

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Mathematica [B]  time = 0.00, size = 70, normalized size = 2.19 \begin {gather*} 6 x^3+11 x^4+6 x^5+5 x^6+16 x^7+16 x^8+4 x^9+6 x^{10}+14 x^{11}+6 x^{12}+4 x^{14}+4 x^{15}+x^{18}+2 x \log (\log (4)) \end {gather*}

Antiderivative was successfully verified.

[In]

Integrate[18*x^2 + 44*x^3 + 30*x^4 + 30*x^5 + 112*x^6 + 128*x^7 + 36*x^8 + 60*x^9 + 154*x^10 + 72*x^11 + 56*x^
13 + 60*x^14 + 18*x^17 + 2*Log[Log[4]],x]

[Out]

6*x^3 + 11*x^4 + 6*x^5 + 5*x^6 + 16*x^7 + 16*x^8 + 4*x^9 + 6*x^10 + 14*x^11 + 6*x^12 + 4*x^14 + 4*x^15 + x^18
+ 2*x*Log[Log[4]]

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fricas [B]  time = 0.57, size = 72, normalized size = 2.25 \begin {gather*} x^{18} + 4 \, x^{15} + 4 \, x^{14} + 6 \, x^{12} + 14 \, x^{11} + 6 \, x^{10} + 4 \, x^{9} + 16 \, x^{8} + 16 \, x^{7} + 5 \, x^{6} + 6 \, x^{5} + 11 \, x^{4} + 6 \, x^{3} + 2 \, x \log \left (2 \, \log \relax (2)\right ) \end {gather*}

Verification of antiderivative is not currently implemented for this CAS.

[In]

integrate(2*log(2*log(2))+18*x^17+60*x^14+56*x^13+72*x^11+154*x^10+60*x^9+36*x^8+128*x^7+112*x^6+30*x^5+30*x^4
+44*x^3+18*x^2,x, algorithm="fricas")

[Out]

x^18 + 4*x^15 + 4*x^14 + 6*x^12 + 14*x^11 + 6*x^10 + 4*x^9 + 16*x^8 + 16*x^7 + 5*x^6 + 6*x^5 + 11*x^4 + 6*x^3
+ 2*x*log(2*log(2))

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giac [B]  time = 0.14, size = 72, normalized size = 2.25 \begin {gather*} x^{18} + 4 \, x^{15} + 4 \, x^{14} + 6 \, x^{12} + 14 \, x^{11} + 6 \, x^{10} + 4 \, x^{9} + 16 \, x^{8} + 16 \, x^{7} + 5 \, x^{6} + 6 \, x^{5} + 11 \, x^{4} + 6 \, x^{3} + 2 \, x \log \left (2 \, \log \relax (2)\right ) \end {gather*}

Verification of antiderivative is not currently implemented for this CAS.

[In]

integrate(2*log(2*log(2))+18*x^17+60*x^14+56*x^13+72*x^11+154*x^10+60*x^9+36*x^8+128*x^7+112*x^6+30*x^5+30*x^4
+44*x^3+18*x^2,x, algorithm="giac")

[Out]

x^18 + 4*x^15 + 4*x^14 + 6*x^12 + 14*x^11 + 6*x^10 + 4*x^9 + 16*x^8 + 16*x^7 + 5*x^6 + 6*x^5 + 11*x^4 + 6*x^3
+ 2*x*log(2*log(2))

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maple [B]  time = 0.05, size = 73, normalized size = 2.28

method	result	size
default	\(2 x \ln \left (2 \ln \relax (2)\right )+x^{18}+4 x^{15}+4 x^{14}+6 x^{12}+14 x^{11}+6 x^{10}+4 x^{9}+16 x^{8}+16 x^{7}+5 x^{6}+6 x^{5}+11 x^{4}+6 x^{3}\)	\(73\)
gosper	\(x \left (x^{17}+4 x^{14}+4 x^{13}+6 x^{11}+14 x^{10}+6 x^{9}+4 x^{8}+16 x^{7}+16 x^{6}+5 x^{5}+6 x^{4}+11 x^{3}+6 x^{2}+2 \ln \left (2 \ln \relax (2)\right )\right )\)	\(74\)
risch	\(x^{18}+4 x^{15}+4 x^{14}+6 x^{12}+14 x^{11}+6 x^{10}+4 x^{9}+16 x^{8}+16 x^{7}+5 x^{6}+6 x^{5}+11 x^{4}+6 x^{3}+2 x \ln \relax (2)+2 x \ln \left (\ln \relax (2)\right )\)	\(76\)
norman	\(x^{18}+\left (2 \ln \relax (2)+2 \ln \left (\ln \relax (2)\right )\right ) x +6 x^{3}+11 x^{4}+6 x^{5}+5 x^{6}+16 x^{7}+16 x^{8}+4 x^{9}+6 x^{10}+14 x^{11}+6 x^{12}+4 x^{14}+4 x^{15}\)	\(77\)

Verification of antiderivative is not currently implemented for this CAS.

[In]

int(2*ln(2*ln(2))+18*x^17+60*x^14+56*x^13+72*x^11+154*x^10+60*x^9+36*x^8+128*x^7+112*x^6+30*x^5+30*x^4+44*x^3+
18*x^2,x,method=_RETURNVERBOSE)

[Out]

2*x*ln(2*ln(2))+x^18+4*x^15+4*x^14+6*x^12+14*x^11+6*x^10+4*x^9+16*x^8+16*x^7+5*x^6+6*x^5+11*x^4+6*x^3

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maxima [B]  time = 0.38, size = 72, normalized size = 2.25 \begin {gather*} x^{18} + 4 \, x^{15} + 4 \, x^{14} + 6 \, x^{12} + 14 \, x^{11} + 6 \, x^{10} + 4 \, x^{9} + 16 \, x^{8} + 16 \, x^{7} + 5 \, x^{6} + 6 \, x^{5} + 11 \, x^{4} + 6 \, x^{3} + 2 \, x \log \left (2 \, \log \relax (2)\right ) \end {gather*}

Verification of antiderivative is not currently implemented for this CAS.

[In]

integrate(2*log(2*log(2))+18*x^17+60*x^14+56*x^13+72*x^11+154*x^10+60*x^9+36*x^8+128*x^7+112*x^6+30*x^5+30*x^4
+44*x^3+18*x^2,x, algorithm="maxima")

[Out]

x^18 + 4*x^15 + 4*x^14 + 6*x^12 + 14*x^11 + 6*x^10 + 4*x^9 + 16*x^8 + 16*x^7 + 5*x^6 + 6*x^5 + 11*x^4 + 6*x^3
+ 2*x*log(2*log(2))

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mupad [B]  time = 5.91, size = 71, normalized size = 2.22 \begin {gather*} x^{18}+4\,x^{15}+4\,x^{14}+6\,x^{12}+14\,x^{11}+6\,x^{10}+4\,x^9+16\,x^8+16\,x^7+5\,x^6+6\,x^5+11\,x^4+6\,x^3+\ln \left ({\ln \relax (4)}^2\right )\,x \end {gather*}

Verification of antiderivative is not currently implemented for this CAS.

[In]

int(2*log(2*log(2)) + 18*x^2 + 44*x^3 + 30*x^4 + 30*x^5 + 112*x^6 + 128*x^7 + 36*x^8 + 60*x^9 + 154*x^10 + 72*
x^11 + 56*x^13 + 60*x^14 + 18*x^17,x)

[Out]

x*log(log(4)^2) + 6*x^3 + 11*x^4 + 6*x^5 + 5*x^6 + 16*x^7 + 16*x^8 + 4*x^9 + 6*x^10 + 14*x^11 + 6*x^12 + 4*x^1
4 + 4*x^15 + x^18

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sympy [B]  time = 0.07, size = 76, normalized size = 2.38 \begin {gather*} x^{18} + 4 x^{15} + 4 x^{14} + 6 x^{12} + 14 x^{11} + 6 x^{10} + 4 x^{9} + 16 x^{8} + 16 x^{7} + 5 x^{6} + 6 x^{5} + 11 x^{4} + 6 x^{3} + x \left (2 \log {\left (\log {\relax (2 )} \right )} + 2 \log {\relax (2 )}\right ) \end {gather*}

Verification of antiderivative is not currently implemented for this CAS.

[In]

integrate(2*ln(2*ln(2))+18*x**17+60*x**14+56*x**13+72*x**11+154*x**10+60*x**9+36*x**8+128*x**7+112*x**6+30*x**
5+30*x**4+44*x**3+18*x**2,x)

[Out]

x**18 + 4*x**15 + 4*x**14 + 6*x**12 + 14*x**11 + 6*x**10 + 4*x**9 + 16*x**8 + 16*x**7 + 5*x**6 + 6*x**5 + 11*x
**4 + 6*x**3 + x*(2*log(log(2)) + 2*log(2))

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