3.90.78 \(\int (5+e^8 (40-20 x)+e^{16} (-40 x+15 x^2)) \, dx\) [8978]

Optimal. Leaf size=15 \[ 5 (-4+x) \left (1-e^8 x\right )^2 \]

[Out]

(1-x*exp(4)^2)^2*(5*x-20)

________________________________________________________________________________________

Rubi [B] Leaf count is larger than twice the leaf count of optimal. \(32\) vs. \(2(15)=30\).
time = 0.01, antiderivative size = 32, normalized size of antiderivative = 2.13, number of steps used = 2, number of rules used = 0, integrand size = 24, \(\frac {\text {number of rules}}{\text {integrand size}}\) = 0.000, Rules used = {} \begin {gather*} 5 e^{16} x^3-20 e^{16} x^2+5 x-10 e^8 (2-x)^2 \end {gather*}

Antiderivative was successfully verified.

[In]

Int[5 + E^8*(40 - 20*x) + E^16*(-40*x + 15*x^2),x]

[Out]

-10*E^8*(2 - x)^2 + 5*x - 20*E^16*x^2 + 5*E^16*x^3

Rubi steps

\begin {gather*} \begin {aligned} \text {integral} &=-10 e^8 (2-x)^2+5 x+e^{16} \int \left (-40 x+15 x^2\right ) \, dx\\ &=-10 e^8 (2-x)^2+5 x-20 e^{16} x^2+5 e^{16} x^3\\ \end {aligned} \end {gather*}

________________________________________________________________________________________

Mathematica [B] Leaf count is larger than twice the leaf count of optimal. \(34\) vs. \(2(15)=30\).
time = 0.00, size = 34, normalized size = 2.27 \begin {gather*} 5 x+40 e^8 x-10 e^8 x^2-20 e^{16} x^2+5 e^{16} x^3 \end {gather*}

Antiderivative was successfully verified.

[In]

Integrate[5 + E^8*(40 - 20*x) + E^16*(-40*x + 15*x^2),x]

[Out]

5*x + 40*E^8*x - 10*E^8*x^2 - 20*E^16*x^2 + 5*E^16*x^3

________________________________________________________________________________________

Maple [B] Leaf count of result is larger than twice the leaf count of optimal. \(45\) vs. \(2(17)=34\).
time = 0.41, size = 46, normalized size = 3.07

method	result	size
risch	\(5 x^{3} {\mathrm e}^{16}-20 x^{2} {\mathrm e}^{16}-10 x^{2} {\mathrm e}^{8}+40 x \,{\mathrm e}^{8}+5 x\)	\(31\)
gosper	\(5 x \left (x^{2} {\mathrm e}^{16}-4 x \,{\mathrm e}^{16}-2 x \,{\mathrm e}^{8}+8 \,{\mathrm e}^{8}+1\right )\)	\(34\)
norman	\(\left (40 \,{\mathrm e}^{8}+5\right ) x +\left (-20 \,{\mathrm e}^{16}-10 \,{\mathrm e}^{8}\right ) x^{2}+5 x^{3} {\mathrm e}^{16}\)	\(38\)
default	\(5 x^{3} {\mathrm e}^{16}+\frac {5 \left (-3 \,{\mathrm e}^{8}+{\mathrm e}^{8} \left (-8 \,{\mathrm e}^{8}-1\right )\right ) x^{2}}{2}+40 x \,{\mathrm e}^{8}+5 x\)	\(46\)

Verification of antiderivative is not currently implemented for this CAS.

[In]

int((15*x^2-40*x)*exp(4)^4+(-20*x+40)*exp(4)^2+5,x,method=_RETURNVERBOSE)

[Out]

5*x^3*exp(4)^4+5/2*(-3*exp(4)^2+exp(4)^2*(-8*exp(4)^2-1))*x^2+40*x*exp(4)^2+5*x

________________________________________________________________________________________

Maxima [B] Leaf count of result is larger than twice the leaf count of optimal. 28 vs. \(2 (13) = 26\).
time = 0.25, size = 28, normalized size = 1.87 \begin {gather*} 5 \, {\left (x^{3} - 4 \, x^{2}\right )} e^{16} - 10 \, {\left (x^{2} - 4 \, x\right )} e^{8} + 5 \, x \end {gather*}

Verification of antiderivative is not currently implemented for this CAS.

[In]

integrate((15*x^2-40*x)*exp(4)^4+(-20*x+40)*exp(4)^2+5,x, algorithm="maxima")

[Out]

5*(x^3 - 4*x^2)*e^16 - 10*(x^2 - 4*x)*e^8 + 5*x

________________________________________________________________________________________

Fricas [B] Leaf count of result is larger than twice the leaf count of optimal. 28 vs. \(2 (13) = 26\).
time = 0.40, size = 28, normalized size = 1.87 \begin {gather*} 5 \, {\left (x^{3} - 4 \, x^{2}\right )} e^{16} - 10 \, {\left (x^{2} - 4 \, x\right )} e^{8} + 5 \, x \end {gather*}

Verification of antiderivative is not currently implemented for this CAS.

[In]

integrate((15*x^2-40*x)*exp(4)^4+(-20*x+40)*exp(4)^2+5,x, algorithm="fricas")

[Out]

5*(x^3 - 4*x^2)*e^16 - 10*(x^2 - 4*x)*e^8 + 5*x

________________________________________________________________________________________

Sympy [B] Leaf count of result is larger than twice the leaf count of optimal. 31 vs. \(2 (12) = 24\).
time = 0.01, size = 31, normalized size = 2.07 \begin {gather*} 5 x^{3} e^{16} + x^{2} \left (- 20 e^{16} - 10 e^{8}\right ) + x \left (5 + 40 e^{8}\right ) \end {gather*}

Verification of antiderivative is not currently implemented for this CAS.

[In]

integrate((15*x**2-40*x)*exp(4)**4+(-20*x+40)*exp(4)**2+5,x)

[Out]

5*x**3*exp(16) + x**2*(-20*exp(16) - 10*exp(8)) + x*(5 + 40*exp(8))

________________________________________________________________________________________

Giac [B] Leaf count of result is larger than twice the leaf count of optimal. 28 vs. \(2 (13) = 26\).
time = 0.41, size = 28, normalized size = 1.87 \begin {gather*} 5 \, {\left (x^{3} - 4 \, x^{2}\right )} e^{16} - 10 \, {\left (x^{2} - 4 \, x\right )} e^{8} + 5 \, x \end {gather*}

Verification of antiderivative is not currently implemented for this CAS.

[In]

integrate((15*x^2-40*x)*exp(4)^4+(-20*x+40)*exp(4)^2+5,x, algorithm="giac")

[Out]

5*(x^3 - 4*x^2)*e^16 - 10*(x^2 - 4*x)*e^8 + 5*x

________________________________________________________________________________________

Mupad [B]
time = 0.05, size = 30, normalized size = 2.00 \begin {gather*} 5\,{\mathrm {e}}^{16}\,x^3+\left (-10\,{\mathrm {e}}^8-20\,{\mathrm {e}}^{16}\right )\,x^2+\left (40\,{\mathrm {e}}^8+5\right )\,x \end {gather*}

Verification of antiderivative is not currently implemented for this CAS.

[In]

int(5 - exp(8)*(20*x - 40) - exp(16)*(40*x - 15*x^2),x)

[Out]

5*x^3*exp(16) - x^2*(10*exp(8) + 20*exp(16)) + x*(40*exp(8) + 5)

________________________________________________________________________________________