3.17.91 $\int (-16+16x+96x^2-112x^3-80x^4+96x^5+e^{32}(2x-6x^2+4x^3)+e^{16}(4-24x+12x^2+48x^3-40x^4))dx$

Optimal. Leaf size=27 $${(2-e^{16}-\frac{2}{x}+4x)}^2{(x-x^2)}^2$$

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Rubi [B]  time = 0.05, antiderivative size = 89, normalized size of antiderivative = 3.30, number of steps used = 3, number of rules used = 0, integrand size = 67, $\frac{\text{number of rules}}{\text{integrand size}}$ = 0.000, Rules used = {} $$\begin{array}{c}16x^6-8e^{16}{x}^5-16x^5+e^{32}{x}^4+12e^{16}{x}^4-28x^4-2e^{32}{x}^3+4e^{16}{x}^3+32x^3+e^{32}{x}^2-12e^{16}{x}^2+8x^2+4e^{16}x-16x\end{array}$$

Antiderivative was successfully verified.

[In]

Int[-16 + 16*x + 96*x^2 - 112*x^3 - 80*x^4 + 96*x^5 + E^32*(2*x - 6*x^2 + 4*x^3) + E^16*(4 - 24*x + 12*x^2 + 4
8*x^3 - 40*x^4),x]

[Out]

-16*x + 4*E^16*x + 8*x^2 - 12*E^16*x^2 + E^32*x^2 + 32*x^3 + 4*E^16*x^3 - 2*E^32*x^3 - 28*x^4 + 12*E^16*x^4 +
E^32*x^4 - 16*x^5 - 8*E^16*x^5 + 16*x^6

Rubi steps

$$\begin{array}{c}\begin{array}{rl}\text{integral}& =-16x+8x^2+32x^3-28x^4-16x^5+16x^6+e^{16}\int (4-24x+12x^2+48x^3-40x^4)dx+e^{32}\int (2x-6x^2+4x^3)dx\\ & =-16x+4e^{16}x+8x^2-12e^{16}{x}^2+e^{32}{x}^2+32x^3+4e^{16}{x}^3-2e^{32}{x}^3-28x^4+12e^{16}{x}^4+e^{32}{x}^4-16x^5-8e^{16}{x}^5+16x^6\end{array}\end{array}$$

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Mathematica [B]  time = 0.01, size = 89, normalized size = 3.30 $$\begin{array}{c}-16x+4e^{16}x+8x^2-12e^{16}{x}^2+e^{32}{x}^2+32x^3+4e^{16}{x}^3-2e^{32}{x}^3-28x^4+12e^{16}{x}^4+e^{32}{x}^4-16x^5-8e^{16}{x}^5+16x^6\end{array}$$

Antiderivative was successfully verified.

[In]

Integrate[-16 + 16*x + 96*x^2 - 112*x^3 - 80*x^4 + 96*x^5 + E^32*(2*x - 6*x^2 + 4*x^3) + E^16*(4 - 24*x + 12*x
^2 + 48*x^3 - 40*x^4),x]

[Out]

-16*x + 4*E^16*x + 8*x^2 - 12*E^16*x^2 + E^32*x^2 + 32*x^3 + 4*E^16*x^3 - 2*E^32*x^3 - 28*x^4 + 12*E^16*x^4 +
E^32*x^4 - 16*x^5 - 8*E^16*x^5 + 16*x^6

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fricas [B]  time = 0.83, size = 72, normalized size = 2.67 $$\begin{array}{c}16x^6-16x^5-28x^4+32x^3+8x^2+(x^4-2x^3+x^2)e^{32}-4(2x^5-3x^4-x^3+3x^2-x)e^{16}-16x\end{array}$$

Verification of antiderivative is not currently implemented for this CAS.

[In]

integrate((4*x^3-6*x^2+2*x)*exp(16)^2+(-40*x^4+48*x^3+12*x^2-24*x+4)*exp(16)+96*x^5-80*x^4-112*x^3+96*x^2+16*x
-16,x, algorithm="fricas")

[Out]

16*x^6 - 16*x^5 - 28*x^4 + 32*x^3 + 8*x^2 + (x^4 - 2*x^3 + x^2)*e^32 - 4*(2*x^5 - 3*x^4 - x^3 + 3*x^2 - x)*e^1
6 - 16*x

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giac [B]  time = 0.33, size = 72, normalized size = 2.67 $$\begin{array}{c}16x^6-16x^5-28x^4+32x^3+8x^2+(x^4-2x^3+x^2)e^{32}-4(2x^5-3x^4-x^3+3x^2-x)e^{16}-16x\end{array}$$

Verification of antiderivative is not currently implemented for this CAS.

[In]

integrate((4*x^3-6*x^2+2*x)*exp(16)^2+(-40*x^4+48*x^3+12*x^2-24*x+4)*exp(16)+96*x^5-80*x^4-112*x^3+96*x^2+16*x
-16,x, algorithm="giac")

[Out]

16*x^6 - 16*x^5 - 28*x^4 + 32*x^3 + 8*x^2 + (x^4 - 2*x^3 + x^2)*e^32 - 4*(2*x^5 - 3*x^4 - x^3 + 3*x^2 - x)*e^1
6 - 16*x

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maple [B]  time = 0.03, size = 69, normalized size = 2.56

method	result	size
norman	$(-8{\mathrm{e}}^{16}-16)x^5+(4{\mathrm{e}}^{16}-16)x+(-2{\mathrm{e}}^{32}+4{\mathrm{e}}^{16}+32)x^3+({\mathrm{e}}^{32}-12{\mathrm{e}}^{16}+8)x^2+({\mathrm{e}}^{32}+12{\mathrm{e}}^{16}-28)x^4+16x^6$	$69$
default	${\mathrm{e}}^{32}(x^4-2x^3+x^2)+{\mathrm{e}}^{16}(-8x^5+12x^4+4x^3-12x^2+4x)+16x^6-16x^5-28x^4+32x^3+8x^2-16x$	$74$
gosper	$x({\mathrm{e}}^{32}{x}^3-8{\mathrm{e}}^{16}{x}^4+16x^5-2{\mathrm{e}}^{32}{x}^2+12x^3{\mathrm{e}}^{16}-16x^4+x{\mathrm{e}}^{32}+4x^2{\mathrm{e}}^{16}-28x^3-12x{\mathrm{e}}^{16}+32x^2+4{\mathrm{e}}^{16}+8x-16)$	$81$
risch	$x^4{\mathrm{e}}^{32}-2{\mathrm{e}}^{32}{x}^3+{\mathrm{e}}^{32}{x}^2-8{\mathrm{e}}^{16}{x}^5+12{\mathrm{e}}^{16}{x}^4+4x^3{\mathrm{e}}^{16}-12x^2{\mathrm{e}}^{16}+4x{\mathrm{e}}^{16}+16x^6-16x^5-28x^4+32x^3+8x^2-16x$	$82$

Verification of antiderivative is not currently implemented for this CAS.

[In]

int((4*x^3-6*x^2+2*x)*exp(16)^2+(-40*x^4+48*x^3+12*x^2-24*x+4)*exp(16)+96*x^5-80*x^4-112*x^3+96*x^2+16*x-16,x,
method=_RETURNVERBOSE)

[Out]

(-8*exp(16)-16)*x^5+(4*exp(16)-16)*x+(-2*exp(16)^2+4*exp(16)+32)*x^3+(exp(16)^2-12*exp(16)+8)*x^2+(exp(16)^2+1
2*exp(16)-28)*x^4+16*x^6

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maxima [B]  time = 0.39, size = 72, normalized size = 2.67 $$\begin{array}{c}16x^6-16x^5-28x^4+32x^3+8x^2+(x^4-2x^3+x^2)e^{32}-4(2x^5-3x^4-x^3+3x^2-x)e^{16}-16x\end{array}$$

Verification of antiderivative is not currently implemented for this CAS.

[In]

integrate((4*x^3-6*x^2+2*x)*exp(16)^2+(-40*x^4+48*x^3+12*x^2-24*x+4)*exp(16)+96*x^5-80*x^4-112*x^3+96*x^2+16*x
-16,x, algorithm="maxima")

[Out]

16*x^6 - 16*x^5 - 28*x^4 + 32*x^3 + 8*x^2 + (x^4 - 2*x^3 + x^2)*e^32 - 4*(2*x^5 - 3*x^4 - x^3 + 3*x^2 - x)*e^1
6 - 16*x

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mupad [B]  time = 0.08, size = 63, normalized size = 2.33 $$\begin{array}{c}16x^6+(-8{\mathrm{e}}^{16}-16)x^5+(12{\mathrm{e}}^{16}+{\mathrm{e}}^{32}-28)x^4+(4{\mathrm{e}}^{16}-2{\mathrm{e}}^{32}+32)x^3+({\mathrm{e}}^{32}-12{\mathrm{e}}^{16}+8)x^2+(4{\mathrm{e}}^{16}-16)x\end{array}$$

Verification of antiderivative is not currently implemented for this CAS.

[In]

int(16*x + exp(32)*(2*x - 6*x^2 + 4*x^3) + exp(16)*(12*x^2 - 24*x + 48*x^3 - 40*x^4 + 4) + 96*x^2 - 112*x^3 -
80*x^4 + 96*x^5 - 16,x)

[Out]

x^3*(4*exp(16) - 2*exp(32) + 32) - x^5*(8*exp(16) + 16) + x^2*(exp(32) - 12*exp(16) + 8) + x^4*(12*exp(16) + e
xp(32) - 28) + 16*x^6 + x*(4*exp(16) - 16)

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sympy [B]  time = 0.07, size = 66, normalized size = 2.44 $$\begin{array}{c}16x^6+x^5(-8e^{16}-16)+x^4(-28+12e^{16}+e^{32})+x^3(-2e^{32}+32+4e^{16})+x^2(-12e^{16}+8+e^{32})+x(-16+4e^{16})\end{array}$$

Verification of antiderivative is not currently implemented for this CAS.

[In]

integrate((4*x**3-6*x**2+2*x)*exp(16)**2+(-40*x**4+48*x**3+12*x**2-24*x+4)*exp(16)+96*x**5-80*x**4-112*x**3+96
*x**2+16*x-16,x)

[Out]

16*x**6 + x**5*(-8*exp(16) - 16) + x**4*(-28 + 12*exp(16) + exp(32)) + x**3*(-2*exp(32) + 32 + 4*exp(16)) + x*
*2*(-12*exp(16) + 8 + exp(32)) + x*(-16 + 4*exp(16))

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