\(\int (-1-20 e^2+9 x^8) \, dx\) [7524]

Optimal result

Integrand size = 12, antiderivative size = 12 \[ \int \left (-1-20 e^2+9 x^8\right ) \, dx=x \left (-1-20 e^2+x^8\right ) \]

[Out]

(x^8-exp(ln(20)+2)-1)*x

Rubi [A] (verified)

Time = 0.00 (sec) , antiderivative size = 14, normalized size of antiderivative = 1.17, number of steps used = 1, number of rules used = 0, \(\frac {\text {number of rules}}{\text {integrand size}}\) = 0.000, Rules used = {} \[ \int \left (-1-20 e^2+9 x^8\right ) \, dx=x^9-\left (1+20 e^2\right ) x \]

[In]

Int[-1 - 20*E^2 + 9*x^8,x]

[Out]

-((1 + 20*E^2)*x) + x^9

Rubi steps \begin{align*} \text {integral}& = -\left (\left (1+20 e^2\right ) x\right )+x^9 \\ \end{align*}

Mathematica [A] (verified)

Time = 0.00 (sec) , antiderivative size = 13, normalized size of antiderivative = 1.08 \[ \int \left (-1-20 e^2+9 x^8\right ) \, dx=-x-20 e^2 x+x^9 \]

[In]

Integrate[-1 - 20*E^2 + 9*x^8,x]

[Out]

-x - 20*E^2*x + x^9

Maple [A] (verified)

Time = 0.04 (sec) , antiderivative size = 13, normalized size of antiderivative = 1.08

method	result	size
norman	\(x^{9}+\left (-20 \,{\mathrm e}^{2}-1\right ) x\)	\(13\)
risch	\(-20 \,{\mathrm e}^{2} x +x^{9}-x\)	\(13\)
gosper	\(-x \left (-x^{8}+{\mathrm e}^{\ln \left (20\right )+2}+1\right )\)	\(16\)
default	\(-x \,{\mathrm e}^{\ln \left (20\right )+2}+x^{9}-x\)	\(16\)
parallelrisch	\(x^{9}+\left (-{\mathrm e}^{\ln \left (20\right )+2}-1\right ) x\)	\(16\)
parts	\(-x \,{\mathrm e}^{\ln \left (20\right )+2}+x^{9}-x\)	\(16\)

[In]

int(-exp(ln(20)+2)+9*x^8-1,x,method=_RETURNVERBOSE)

[Out]

x^9+(-20*exp(2)-1)*x

Fricas [A] (verification not implemented)

none

Time = 0.24 (sec) , antiderivative size = 15, normalized size of antiderivative = 1.25 \[ \int \left (-1-20 e^2+9 x^8\right ) \, dx=x^{9} - x e^{\left (\log \left (20\right ) + 2\right )} - x \]

[In]

integrate(-exp(log(20)+2)+9*x^8-1,x, algorithm="fricas")

[Out]

x^9 - x*e^(log(20) + 2) - x

Sympy [A] (verification not implemented)

Time = 0.02 (sec) , antiderivative size = 12, normalized size of antiderivative = 1.00 \[ \int \left (-1-20 e^2+9 x^8\right ) \, dx=x^{9} + x \left (- 20 e^{2} - 1\right ) \]

[In]

integrate(-exp(ln(20)+2)+9*x**8-1,x)

[Out]

x**9 + x*(-20*exp(2) - 1)

Maxima [A] (verification not implemented)

none

Time = 0.23 (sec) , antiderivative size = 12, normalized size of antiderivative = 1.00 \[ \int \left (-1-20 e^2+9 x^8\right ) \, dx=x^{9} - 20 \, x e^{2} - x \]

[In]

integrate(-exp(log(20)+2)+9*x^8-1,x, algorithm="maxima")

[Out]

x^9 - 20*x*e^2 - x

Giac [A] (verification not implemented)

none

Time = 0.25 (sec) , antiderivative size = 15, normalized size of antiderivative = 1.25 \[ \int \left (-1-20 e^2+9 x^8\right ) \, dx=x^{9} - x e^{\left (\log \left (20\right ) + 2\right )} - x \]

[In]

integrate(-exp(log(20)+2)+9*x^8-1,x, algorithm="giac")

[Out]

x^9 - x*e^(log(20) + 2) - x

Mupad [B] (verification not implemented)

Time = 12.37 (sec) , antiderivative size = 13, normalized size of antiderivative = 1.08 \[ \int \left (-1-20 e^2+9 x^8\right ) \, dx=x^9-x\,\left (20\,{\mathrm {e}}^2+1\right ) \]

[In]

int(9*x^8 - exp(log(20) + 2) - 1,x)

[Out]

x^9 - x*(20*exp(2) + 1)