\(\int (-160+e (10-4 x)+64 x) \, dx\) [9907]

Optimal result

Integrand size = 12, antiderivative size = 11 \[ \int (-160+e (10-4 x)+64 x) \, dx=2 (-16+e) (5-x) x \]

[Out]

2*(5-x)*x*(exp(1)-16)

Rubi [A] (verified)

Time = 0.00 (sec) , antiderivative size = 21, normalized size of antiderivative = 1.91, number of steps used = 1, number of rules used = 0, \(\frac {\text {number of rules}}{\text {integrand size}}\) = 0.000, Rules used = {} \[ \int (-160+e (10-4 x)+64 x) \, dx=32 x^2-\frac {1}{2} e (5-2 x)^2-160 x \]

[In]

Int[-160 + E*(10 - 4*x) + 64*x,x]

[Out]

-1/2*(E*(5 - 2*x)^2) - 160*x + 32*x^2

Rubi steps \begin{align*} \text {integral}& = -\frac {1}{2} e (5-2 x)^2-160 x+32 x^2 \\ \end{align*}

Mathematica [A] (verified)

Time = 0.00 (sec) , antiderivative size = 12, normalized size of antiderivative = 1.09 \[ \int (-160+e (10-4 x)+64 x) \, dx=-2 (-16+e) \left (-5 x+x^2\right ) \]

[In]

Integrate[-160 + E*(10 - 4*x) + 64*x,x]

[Out]

-2*(-16 + E)*(-5*x + x^2)

Maple [A] (verified)

Time = 0.10 (sec) , antiderivative size = 11, normalized size of antiderivative = 1.00

method	result	size
gosper	\(-2 \left ({\mathrm e}-16\right ) \left (-5+x \right ) x\)	\(11\)
default	\(-2 \left ({\mathrm e}-16\right ) \left (x^{2}-5 x \right )\)	\(14\)
norman	\(\left (-2 \,{\mathrm e}+32\right ) x^{2}+\left (10 \,{\mathrm e}-160\right ) x\)	\(20\)
risch	\(-2 x^{2} {\mathrm e}+10 x \,{\mathrm e}+32 x^{2}-160 x\)	\(22\)
parallelrisch	\(-2 x^{2} {\mathrm e}+10 x \,{\mathrm e}+32 x^{2}-160 x\)	\(22\)
parts	\(-2 x^{2} {\mathrm e}+10 x \,{\mathrm e}+32 x^{2}-160 x\)	\(22\)

[In]

int((10-4*x)*exp(1)+64*x-160,x,method=_RETURNVERBOSE)

[Out]

-2*(exp(1)-16)*(-5+x)*x

Fricas [A] (verification not implemented)

none

Time = 0.25 (sec) , antiderivative size = 20, normalized size of antiderivative = 1.82 \[ \int (-160+e (10-4 x)+64 x) \, dx=32 \, x^{2} - 2 \, {\left (x^{2} - 5 \, x\right )} e - 160 \, x \]

[In]

integrate((10-4*x)*exp(1)+64*x-160,x, algorithm="fricas")

[Out]

32*x^2 - 2*(x^2 - 5*x)*e - 160*x

Sympy [A] (verification not implemented)

Time = 0.03 (sec) , antiderivative size = 17, normalized size of antiderivative = 1.55 \[ \int (-160+e (10-4 x)+64 x) \, dx=x^{2} \cdot \left (32 - 2 e\right ) + x \left (-160 + 10 e\right ) \]

[In]

integrate((10-4*x)*exp(1)+64*x-160,x)

[Out]

x**2*(32 - 2*E) + x*(-160 + 10*E)

Maxima [A] (verification not implemented)

none

Time = 0.21 (sec) , antiderivative size = 20, normalized size of antiderivative = 1.82 \[ \int (-160+e (10-4 x)+64 x) \, dx=32 \, x^{2} - 2 \, {\left (x^{2} - 5 \, x\right )} e - 160 \, x \]

[In]

integrate((10-4*x)*exp(1)+64*x-160,x, algorithm="maxima")

[Out]

32*x^2 - 2*(x^2 - 5*x)*e - 160*x

Giac [A] (verification not implemented)

none

Time = 0.27 (sec) , antiderivative size = 20, normalized size of antiderivative = 1.82 \[ \int (-160+e (10-4 x)+64 x) \, dx=32 \, x^{2} - 2 \, {\left (x^{2} - 5 \, x\right )} e - 160 \, x \]

[In]

integrate((10-4*x)*exp(1)+64*x-160,x, algorithm="giac")

[Out]

32*x^2 - 2*(x^2 - 5*x)*e - 160*x

Mupad [B] (verification not implemented)

Time = 15.32 (sec) , antiderivative size = 10, normalized size of antiderivative = 0.91 \[ \int (-160+e (10-4 x)+64 x) \, dx=-2\,x\,\left (\mathrm {e}-16\right )\,\left (x-5\right ) \]

[In]

int(64*x - exp(1)*(4*x - 10) - 160,x)

[Out]

-2*x*(exp(1) - 16)*(x - 5)