Integrand size = 56, antiderivative size = 26 \[ \int \left (-1+486 x^5+e^{7 x} \left (2430 x^4+4374 x^5+1134 x^6\right )+e^{14 x} \left (2916 x^3+12636 x^4+7290 x^5+1134 x^6\right )\right ) \, dx=-1-x+81 x^4 \left (-e^{7 x} (-3-x)+x\right )^2 \] Output:
81*(x-exp(7*x)*(-3-x))^2*x^4-x-1
Time = 0.25 (sec) , antiderivative size = 52, normalized size of antiderivative = 2.00 \[ \int \left (-1+486 x^5+e^{7 x} \left (2430 x^4+4374 x^5+1134 x^6\right )+e^{14 x} \left (2916 x^3+12636 x^4+7290 x^5+1134 x^6\right )\right ) \, dx=-x+81 x^6+162 e^{14 x} \left (\frac {9 x^4}{2}+3 x^5+\frac {x^6}{2}\right )+162 e^{7 x} \left (3 x^5+x^6\right ) \] Input:
Integrate[-1 + 486*x^5 + E^(7*x)*(2430*x^4 + 4374*x^5 + 1134*x^6) + E^(14* x)*(2916*x^3 + 12636*x^4 + 7290*x^5 + 1134*x^6),x]
Output:
-x + 81*x^6 + 162*E^(14*x)*((9*x^4)/2 + 3*x^5 + x^6/2) + 162*E^(7*x)*(3*x^ 5 + x^6)
Leaf count is larger than twice the leaf count of optimal. \(59\) vs. \(2(26)=52\).
Time = 0.63 (sec) , antiderivative size = 59, normalized size of antiderivative = 2.27, number of steps used = 1, number of rules used = 1, \(\frac {\text {number of rules}}{\text {integrand size}}\) = 0.018, Rules used = {2009}
Below are the steps used by Rubi to obtain the solution. The rule number used for the transformation is given above next to the arrow. The rules definitions used are listed below.
\(\displaystyle \int \left (486 x^5+e^{7 x} \left (1134 x^6+4374 x^5+2430 x^4\right )+e^{14 x} \left (1134 x^6+7290 x^5+12636 x^4+2916 x^3\right )-1\right ) \, dx\) |
\(\Big \downarrow \) 2009 |
\(\displaystyle 162 e^{7 x} x^6+81 e^{14 x} x^6+81 x^6+486 e^{7 x} x^5+486 e^{14 x} x^5+729 e^{14 x} x^4-x\) |
Input:
Int[-1 + 486*x^5 + E^(7*x)*(2430*x^4 + 4374*x^5 + 1134*x^6) + E^(14*x)*(29 16*x^3 + 12636*x^4 + 7290*x^5 + 1134*x^6),x]
Output:
-x + 729*E^(14*x)*x^4 + 486*E^(7*x)*x^5 + 486*E^(14*x)*x^5 + 81*x^6 + 162* E^(7*x)*x^6 + 81*E^(14*x)*x^6
Time = 0.43 (sec) , antiderivative size = 49, normalized size of antiderivative = 1.88
method | result | size |
risch | \(\left (81 x^{6}+486 x^{5}+729 x^{4}\right ) {\mathrm e}^{14 x}+\left (162 x^{6}+486 x^{5}\right ) {\mathrm e}^{7 x}+81 x^{6}-x\) | \(49\) |
derivativedivides | \(81 \,{\mathrm e}^{14 x} x^{6}+162 \,{\mathrm e}^{7 x} x^{6}+486 \,{\mathrm e}^{14 x} x^{5}+486 \,{\mathrm e}^{7 x} x^{5}+81 x^{6}+729 \,{\mathrm e}^{14 x} x^{4}-x\) | \(61\) |
default | \(81 \,{\mathrm e}^{14 x} x^{6}+162 \,{\mathrm e}^{7 x} x^{6}+486 \,{\mathrm e}^{14 x} x^{5}+486 \,{\mathrm e}^{7 x} x^{5}+81 x^{6}+729 \,{\mathrm e}^{14 x} x^{4}-x\) | \(61\) |
norman | \(81 \,{\mathrm e}^{14 x} x^{6}+162 \,{\mathrm e}^{7 x} x^{6}+486 \,{\mathrm e}^{14 x} x^{5}+486 \,{\mathrm e}^{7 x} x^{5}+81 x^{6}+729 \,{\mathrm e}^{14 x} x^{4}-x\) | \(61\) |
parallelrisch | \(81 \,{\mathrm e}^{14 x} x^{6}+162 \,{\mathrm e}^{7 x} x^{6}+486 \,{\mathrm e}^{14 x} x^{5}+486 \,{\mathrm e}^{7 x} x^{5}+81 x^{6}+729 \,{\mathrm e}^{14 x} x^{4}-x\) | \(61\) |
parts | \(81 \,{\mathrm e}^{14 x} x^{6}+162 \,{\mathrm e}^{7 x} x^{6}+486 \,{\mathrm e}^{14 x} x^{5}+486 \,{\mathrm e}^{7 x} x^{5}+81 x^{6}+729 \,{\mathrm e}^{14 x} x^{4}-x\) | \(61\) |
orering | \(\frac {\left (1867795524 x^{14}+21613062492 x^{13}+92055636540 x^{12}+169816919580 x^{11}+111618480330 x^{10}-8330120638 x^{9}-10316021352 x^{8}+5117817936 x^{7}+16668734985 x^{6}+36280909035 x^{5}+35339821209 x^{4}+15607196010 x^{3}+2640616794 x^{2}-34334280 x -36556920\right ) \left (\left (1134 x^{6}+7290 x^{5}+12636 x^{4}+2916 x^{3}\right ) {\mathrm e}^{14 x}+\left (1134 x^{6}+4374 x^{5}+2430 x^{4}\right ) {\mathrm e}^{7 x}+486 x^{5}-1\right )}{11206773144 x^{13}+117671118012 x^{12}+436263668820 x^{11}+643245907500 x^{10}+261709192080 x^{9}-38838355108 x^{8}-19674475884 x^{7}+2619515010 x^{6}-2520072450 x^{5}-2206927170 x^{4}-958661676 x^{3}-160412868 x^{2}+2222640 x +2222640}-\frac {x \left (400241898 x^{13}+3945241566 x^{12}+13207982634 x^{11}+15560424810 x^{10}+1102707270 x^{9}-2283869616 x^{8}+406518112 x^{7}+659713509 x^{6}+3163343862 x^{5}+5852698866 x^{4}+4245032421 x^{3}+1100529342 x^{2}+9307872 x -18278460\right ) \left (\left (6804 x^{5}+36450 x^{4}+50544 x^{3}+8748 x^{2}\right ) {\mathrm e}^{14 x}+14 \left (1134 x^{6}+7290 x^{5}+12636 x^{4}+2916 x^{3}\right ) {\mathrm e}^{14 x}+\left (6804 x^{5}+21870 x^{4}+9720 x^{3}\right ) {\mathrm e}^{7 x}+7 \left (1134 x^{6}+4374 x^{5}+2430 x^{4}\right ) {\mathrm e}^{7 x}+2430 x^{4}\right )}{686 \left (16336404 x^{13}+171532242 x^{12}+635952870 x^{11}+937676250 x^{10}+381500280 x^{9}-56615678 x^{8}-28679994 x^{7}+3818535 x^{6}-3673575 x^{5}-3217095 x^{4}-1397466 x^{3}-233838 x^{2}+3240 x +3240\right )}+\frac {x^{2} \left (19059138 x^{12}+171532242 x^{11}+490092120 x^{10}+367569090 x^{9}-210039480 x^{8}+31270624 x^{7}+31414929 x^{5}+134179983 x^{4}+214804716 x^{3}+110085237 x^{2}+10468926 x -3046410\right ) \left (\left (34020 x^{4}+145800 x^{3}+151632 x^{2}+17496 x \right ) {\mathrm e}^{14 x}+28 \left (6804 x^{5}+36450 x^{4}+50544 x^{3}+8748 x^{2}\right ) {\mathrm e}^{14 x}+196 \left (1134 x^{6}+7290 x^{5}+12636 x^{4}+2916 x^{3}\right ) {\mathrm e}^{14 x}+\left (34020 x^{4}+87480 x^{3}+29160 x^{2}\right ) {\mathrm e}^{7 x}+14 \left (6804 x^{5}+21870 x^{4}+9720 x^{3}\right ) {\mathrm e}^{7 x}+49 \left (1134 x^{6}+4374 x^{5}+2430 x^{4}\right ) {\mathrm e}^{7 x}+9720 x^{3}\right )}{11206773144 x^{13}+117671118012 x^{12}+436263668820 x^{11}+643245907500 x^{10}+261709192080 x^{9}-38838355108 x^{8}-19674475884 x^{7}+2619515010 x^{6}-2520072450 x^{5}-2206927170 x^{4}-958661676 x^{3}-160412868 x^{2}+2222640 x +2222640}\) | \(720\) |
Input:
int((1134*x^6+7290*x^5+12636*x^4+2916*x^3)*exp(7*x)^2+(1134*x^6+4374*x^5+2 430*x^4)*exp(7*x)+486*x^5-1,x,method=_RETURNVERBOSE)
Output:
(81*x^6+486*x^5+729*x^4)*exp(7*x)^2+(162*x^6+486*x^5)*exp(7*x)+81*x^6-x
Time = 0.07 (sec) , antiderivative size = 44, normalized size of antiderivative = 1.69 \[ \int \left (-1+486 x^5+e^{7 x} \left (2430 x^4+4374 x^5+1134 x^6\right )+e^{14 x} \left (2916 x^3+12636 x^4+7290 x^5+1134 x^6\right )\right ) \, dx=81 \, x^{6} + 81 \, {\left (x^{6} + 6 \, x^{5} + 9 \, x^{4}\right )} e^{\left (14 \, x\right )} + 162 \, {\left (x^{6} + 3 \, x^{5}\right )} e^{\left (7 \, x\right )} - x \] Input:
integrate((1134*x^6+7290*x^5+12636*x^4+2916*x^3)*exp(7*x)^2+(1134*x^6+4374 *x^5+2430*x^4)*exp(7*x)+486*x^5-1,x, algorithm="fricas")
Output:
81*x^6 + 81*(x^6 + 6*x^5 + 9*x^4)*e^(14*x) + 162*(x^6 + 3*x^5)*e^(7*x) - x
Leaf count of result is larger than twice the leaf count of optimal. 41 vs. \(2 (20) = 40\).
Time = 0.07 (sec) , antiderivative size = 41, normalized size of antiderivative = 1.58 \[ \int \left (-1+486 x^5+e^{7 x} \left (2430 x^4+4374 x^5+1134 x^6\right )+e^{14 x} \left (2916 x^3+12636 x^4+7290 x^5+1134 x^6\right )\right ) \, dx=81 x^{6} - x + \left (162 x^{6} + 486 x^{5}\right ) e^{7 x} + \left (81 x^{6} + 486 x^{5} + 729 x^{4}\right ) e^{14 x} \] Input:
integrate((1134*x**6+7290*x**5+12636*x**4+2916*x**3)*exp(7*x)**2+(1134*x** 6+4374*x**5+2430*x**4)*exp(7*x)+486*x**5-1,x)
Output:
81*x**6 - x + (162*x**6 + 486*x**5)*exp(7*x) + (81*x**6 + 486*x**5 + 729*x **4)*exp(14*x)
Time = 0.05 (sec) , antiderivative size = 44, normalized size of antiderivative = 1.69 \[ \int \left (-1+486 x^5+e^{7 x} \left (2430 x^4+4374 x^5+1134 x^6\right )+e^{14 x} \left (2916 x^3+12636 x^4+7290 x^5+1134 x^6\right )\right ) \, dx=81 \, x^{6} + 81 \, {\left (x^{6} + 6 \, x^{5} + 9 \, x^{4}\right )} e^{\left (14 \, x\right )} + 162 \, {\left (x^{6} + 3 \, x^{5}\right )} e^{\left (7 \, x\right )} - x \] Input:
integrate((1134*x^6+7290*x^5+12636*x^4+2916*x^3)*exp(7*x)^2+(1134*x^6+4374 *x^5+2430*x^4)*exp(7*x)+486*x^5-1,x, algorithm="maxima")
Output:
81*x^6 + 81*(x^6 + 6*x^5 + 9*x^4)*e^(14*x) + 162*(x^6 + 3*x^5)*e^(7*x) - x
Time = 0.11 (sec) , antiderivative size = 44, normalized size of antiderivative = 1.69 \[ \int \left (-1+486 x^5+e^{7 x} \left (2430 x^4+4374 x^5+1134 x^6\right )+e^{14 x} \left (2916 x^3+12636 x^4+7290 x^5+1134 x^6\right )\right ) \, dx=81 \, x^{6} + 81 \, {\left (x^{6} + 6 \, x^{5} + 9 \, x^{4}\right )} e^{\left (14 \, x\right )} + 162 \, {\left (x^{6} + 3 \, x^{5}\right )} e^{\left (7 \, x\right )} - x \] Input:
integrate((1134*x^6+7290*x^5+12636*x^4+2916*x^3)*exp(7*x)^2+(1134*x^6+4374 *x^5+2430*x^4)*exp(7*x)+486*x^5-1,x, algorithm="giac")
Output:
81*x^6 + 81*(x^6 + 6*x^5 + 9*x^4)*e^(14*x) + 162*(x^6 + 3*x^5)*e^(7*x) - x
Time = 0.59 (sec) , antiderivative size = 54, normalized size of antiderivative = 2.08 \[ \int \left (-1+486 x^5+e^{7 x} \left (2430 x^4+4374 x^5+1134 x^6\right )+e^{14 x} \left (2916 x^3+12636 x^4+7290 x^5+1134 x^6\right )\right ) \, dx=486\,x^5\,{\mathrm {e}}^{7\,x}-x+162\,x^6\,{\mathrm {e}}^{7\,x}+729\,x^4\,{\mathrm {e}}^{14\,x}+486\,x^5\,{\mathrm {e}}^{14\,x}+81\,x^6\,{\mathrm {e}}^{14\,x}+81\,x^6 \] Input:
int(exp(7*x)*(2430*x^4 + 4374*x^5 + 1134*x^6) + exp(14*x)*(2916*x^3 + 1263 6*x^4 + 7290*x^5 + 1134*x^6) + 486*x^5 - 1,x)
Output:
486*x^5*exp(7*x) - x + 162*x^6*exp(7*x) + 729*x^4*exp(14*x) + 486*x^5*exp( 14*x) + 81*x^6*exp(14*x) + 81*x^6
Time = 0.29 (sec) , antiderivative size = 59, normalized size of antiderivative = 2.27 \[ \int \left (-1+486 x^5+e^{7 x} \left (2430 x^4+4374 x^5+1134 x^6\right )+e^{14 x} \left (2916 x^3+12636 x^4+7290 x^5+1134 x^6\right )\right ) \, dx=x \left (81 e^{14 x} x^{5}+486 e^{14 x} x^{4}+729 e^{14 x} x^{3}+162 e^{7 x} x^{5}+486 e^{7 x} x^{4}+81 x^{5}-1\right ) \] Input:
int((1134*x^6+7290*x^5+12636*x^4+2916*x^3)*exp(7*x)^2+(1134*x^6+4374*x^5+2 430*x^4)*exp(7*x)+486*x^5-1,x)
Output:
x*(81*e**(14*x)*x**5 + 486*e**(14*x)*x**4 + 729*e**(14*x)*x**3 + 162*e**(7 *x)*x**5 + 486*e**(7*x)*x**4 + 81*x**5 - 1)