3.30.31 \(\int \frac {1}{3} (7-90 e^{5/3}-90 x) \, dx\)

Optimal. Leaf size=24 \[ \frac {2}{3}+2 x+\frac {1}{3} \left (x-45 \left (e^{5/3}+x\right )^2\right ) \]

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Rubi [A]  time = 0.00, antiderivative size = 18, normalized size of antiderivative = 0.75, number of steps used = 1, number of rules used = 1, integrand size = 16, \(\frac {\text {number of rules}}{\text {integrand size}}\) = 0.062, Rules used = {9} \begin {gather*} -\frac {1}{540} \left (-90 x-90 e^{5/3}+7\right )^2 \end {gather*}

Antiderivative was successfully verified.

[In]

Int[(7 - 90*E^(5/3) - 90*x)/3,x]

[Out]

-1/540*(7 - 90*E^(5/3) - 90*x)^2

Rule 9

Int[(a_)*((b_) + (c_.)*(x_)), x_Symbol] :> Simp[(a*(b + c*x)^2)/(2*c), x] /; FreeQ[{a, b, c}, x]

Rubi steps

\begin {gather*} \begin {aligned} \text {integral} &=-\frac {1}{540} \left (7-90 e^{5/3}-90 x\right )^2\\ \end {aligned} \end {gather*}

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Mathematica [A]  time = 0.00, size = 19, normalized size = 0.79 \begin {gather*} \frac {7 x}{3}-30 e^{5/3} x-15 x^2 \end {gather*}

Antiderivative was successfully verified.

[In]

Integrate[(7 - 90*E^(5/3) - 90*x)/3,x]

[Out]

(7*x)/3 - 30*E^(5/3)*x - 15*x^2

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fricas [A]  time = 0.47, size = 14, normalized size = 0.58 \begin {gather*} -15 \, x^{2} - 30 \, x e^{\frac {5}{3}} + \frac {7}{3} \, x \end {gather*}

Verification of antiderivative is not currently implemented for this CAS.

[In]

integrate(-30*exp(5/3)-30*x+7/3,x, algorithm="fricas")

[Out]

-15*x^2 - 30*x*e^(5/3) + 7/3*x

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giac [A]  time = 0.19, size = 14, normalized size = 0.58 \begin {gather*} -15 \, x^{2} - 30 \, x e^{\frac {5}{3}} + \frac {7}{3} \, x \end {gather*}

Verification of antiderivative is not currently implemented for this CAS.

[In]

integrate(-30*exp(5/3)-30*x+7/3,x, algorithm="giac")

[Out]

-15*x^2 - 30*x*e^(5/3) + 7/3*x

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maple [A]  time = 0.02, size = 13, normalized size = 0.54

method	result	size
gosper	\(-\frac {x \left (45 x +90 \,{\mathrm e}^{\frac {5}{3}}-7\right )}{3}\)	\(13\)
default	\(-30 x \,{\mathrm e}^{\frac {5}{3}}-15 x^{2}+\frac {7 x}{3}\)	\(15\)
norman	\(\left (-30 \,{\mathrm e}^{\frac {5}{3}}+\frac {7}{3}\right ) x -15 x^{2}\)	\(15\)
risch	\(-30 x \,{\mathrm e}^{\frac {5}{3}}-15 x^{2}+\frac {7 x}{3}\)	\(15\)

Verification of antiderivative is not currently implemented for this CAS.

[In]

int(-30*exp(5/3)-30*x+7/3,x,method=_RETURNVERBOSE)

[Out]

-1/3*x*(45*x+90*exp(5/3)-7)

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maxima [A]  time = 0.40, size = 14, normalized size = 0.58 \begin {gather*} -15 \, x^{2} - 30 \, x e^{\frac {5}{3}} + \frac {7}{3} \, x \end {gather*}

Verification of antiderivative is not currently implemented for this CAS.

[In]

integrate(-30*exp(5/3)-30*x+7/3,x, algorithm="maxima")

[Out]

-15*x^2 - 30*x*e^(5/3) + 7/3*x

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mupad [B]  time = 1.67, size = 15, normalized size = 0.62 \begin {gather*} -15\,x^2+\left (\frac {7}{3}-30\,{\mathrm {e}}^{5/3}\right )\,x \end {gather*}

Verification of antiderivative is not currently implemented for this CAS.

[In]

int(7/3 - 30*exp(5/3) - 30*x,x)

[Out]

- 15*x^2 - x*(30*exp(5/3) - 7/3)

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sympy [A]  time = 0.05, size = 15, normalized size = 0.62 \begin {gather*} - 15 x^{2} + x \left (\frac {7}{3} - 30 e^{\frac {5}{3}}\right ) \end {gather*}

Verification of antiderivative is not currently implemented for this CAS.

[In]

integrate(-30*exp(5/3)-30*x+7/3,x)

[Out]

-15*x**2 + x*(7/3 - 30*exp(5/3))

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