\(\int (-144+2 e^{30}+148 x-24 x^2) \, dx\) [5111]

Optimal result

Integrand size = 15, antiderivative size = 26 \[ \int \left (-144+2 e^{30}+148 x-24 x^2\right ) \, dx=-1+2 \left (2-\left (-9-e^{30}+(9-2 x)^2-x\right ) x\right ) \]

[Out]

3-2*x*((-2*x+9)^2-x-9-exp(15)^2)

Rubi [A] (verified)

Time = 0.01 (sec) , antiderivative size = 21, normalized size of antiderivative = 0.81, number of steps used = 1, number of rules used = 0, \(\frac {\text {number of rules}}{\text {integrand size}}\) = 0.000, Rules used = {} \[ \int \left (-144+2 e^{30}+148 x-24 x^2\right ) \, dx=-8 x^3+74 x^2-2 \left (72-e^{30}\right ) x \]

[In]

Int[-144 + 2*E^30 + 148*x - 24*x^2,x]

[Out]

-2*(72 - E^30)*x + 74*x^2 - 8*x^3

Rubi steps \begin{align*} \text {integral}& = -2 \left (72-e^{30}\right ) x+74 x^2-8 x^3 \\ \end{align*}

Mathematica [A] (verified)

Time = 0.00 (sec) , antiderivative size = 20, normalized size of antiderivative = 0.77 \[ \int \left (-144+2 e^{30}+148 x-24 x^2\right ) \, dx=-144 x+2 e^{30} x+74 x^2-8 x^3 \]

[In]

Integrate[-144 + 2*E^30 + 148*x - 24*x^2,x]

[Out]

-144*x + 2*E^30*x + 74*x^2 - 8*x^3

Maple [A] (verified)

Time = 0.05 (sec) , antiderivative size = 18, normalized size of antiderivative = 0.69

method	result	size
gosper	\(2 x \left ({\mathrm e}^{30}-4 x^{2}+37 x -72\right )\)	\(18\)
risch	\(2 x \,{\mathrm e}^{30}-8 x^{3}+74 x^{2}-144 x\)	\(20\)
default	\(2 x \,{\mathrm e}^{30}-8 x^{3}+74 x^{2}-144 x\)	\(22\)
norman	\(\left (2 \,{\mathrm e}^{30}-144\right ) x +74 x^{2}-8 x^{3}\)	\(22\)
parallelrisch	\(\left (2 \,{\mathrm e}^{30}-144\right ) x +74 x^{2}-8 x^{3}\)	\(22\)
parts	\(2 x \,{\mathrm e}^{30}-8 x^{3}+74 x^{2}-144 x\)	\(22\)

[In]

int(2*exp(15)^2-24*x^2+148*x-144,x,method=_RETURNVERBOSE)

[Out]

2*x*(exp(15)^2-4*x^2+37*x-72)

Fricas [A] (verification not implemented)

none

Time = 0.25 (sec) , antiderivative size = 19, normalized size of antiderivative = 0.73 \[ \int \left (-144+2 e^{30}+148 x-24 x^2\right ) \, dx=-8 \, x^{3} + 74 \, x^{2} + 2 \, x e^{30} - 144 \, x \]

[In]

integrate(2*exp(15)^2-24*x^2+148*x-144,x, algorithm="fricas")

[Out]

-8*x^3 + 74*x^2 + 2*x*e^30 - 144*x

Sympy [A] (verification not implemented)

Time = 0.02 (sec) , antiderivative size = 17, normalized size of antiderivative = 0.65 \[ \int \left (-144+2 e^{30}+148 x-24 x^2\right ) \, dx=- 8 x^{3} + 74 x^{2} + x \left (-144 + 2 e^{30}\right ) \]

[In]

integrate(2*exp(15)**2-24*x**2+148*x-144,x)

[Out]

-8*x**3 + 74*x**2 + x*(-144 + 2*exp(30))

Maxima [A] (verification not implemented)

none

Time = 0.19 (sec) , antiderivative size = 19, normalized size of antiderivative = 0.73 \[ \int \left (-144+2 e^{30}+148 x-24 x^2\right ) \, dx=-8 \, x^{3} + 74 \, x^{2} + 2 \, x e^{30} - 144 \, x \]

[In]

integrate(2*exp(15)^2-24*x^2+148*x-144,x, algorithm="maxima")

[Out]

-8*x^3 + 74*x^2 + 2*x*e^30 - 144*x

Giac [A] (verification not implemented)

none

Time = 0.27 (sec) , antiderivative size = 19, normalized size of antiderivative = 0.73 \[ \int \left (-144+2 e^{30}+148 x-24 x^2\right ) \, dx=-8 \, x^{3} + 74 \, x^{2} + 2 \, x e^{30} - 144 \, x \]

[In]

integrate(2*exp(15)^2-24*x^2+148*x-144,x, algorithm="giac")

[Out]

-8*x^3 + 74*x^2 + 2*x*e^30 - 144*x

Mupad [B] (verification not implemented)

Time = 0.03 (sec) , antiderivative size = 15, normalized size of antiderivative = 0.58 \[ \int \left (-144+2 e^{30}+148 x-24 x^2\right ) \, dx=2\,x\,\left (-4\,x^2+37\,x+{\mathrm {e}}^{30}-72\right ) \]

[In]

int(148*x + 2*exp(30) - 24*x^2 - 144,x)

[Out]

2*x*(37*x + exp(30) - 4*x^2 - 72)