3.47.80 \(\int (-69+20 x+3 x^2+e^5 (15+2 x)) \, dx\)

Optimal. Leaf size=17 \[ 4+x+(15+x) \left (5+x \left (-5+e^5+x\right )\right ) \]

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Rubi [A]  time = 0.00, antiderivative size = 26, normalized size of antiderivative = 1.53, number of steps used = 1, number of rules used = 0, integrand size = 19, \(\frac {\text {number of rules}}{\text {integrand size}}\) = 0.000, Rules used = {} \begin {gather*} x^3+10 x^2-69 x+\frac {1}{4} e^5 (2 x+15)^2 \end {gather*}

Antiderivative was successfully verified.

[In]

Int[-69 + 20*x + 3*x^2 + E^5*(15 + 2*x),x]

[Out]

-69*x + 10*x^2 + x^3 + (E^5*(15 + 2*x)^2)/4

Rubi steps

\begin {gather*} \begin {aligned} \text {integral} &=-69 x+10 x^2+x^3+\frac {1}{4} e^5 (15+2 x)^2\\ \end {aligned} \end {gather*}

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Mathematica [A]  time = 0.00, size = 25, normalized size = 1.47 \begin {gather*} -69 x+15 e^5 x+10 x^2+e^5 x^2+x^3 \end {gather*}

Antiderivative was successfully verified.

[In]

Integrate[-69 + 20*x + 3*x^2 + E^5*(15 + 2*x),x]

[Out]

-69*x + 15*E^5*x + 10*x^2 + E^5*x^2 + x^3

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fricas [A]  time = 0.59, size = 22, normalized size = 1.29 \begin {gather*} x^{3} + 10 \, x^{2} + {\left (x^{2} + 15 \, x\right )} e^{5} - 69 \, x \end {gather*}

Verification of antiderivative is not currently implemented for this CAS.

[In]

integrate((2*x+15)*exp(5)+3*x^2+20*x-69,x, algorithm="fricas")

[Out]

x^3 + 10*x^2 + (x^2 + 15*x)*e^5 - 69*x

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giac [A]  time = 0.20, size = 22, normalized size = 1.29 \begin {gather*} x^{3} + 10 \, x^{2} + {\left (x^{2} + 15 \, x\right )} e^{5} - 69 \, x \end {gather*}

Verification of antiderivative is not currently implemented for this CAS.

[In]

integrate((2*x+15)*exp(5)+3*x^2+20*x-69,x, algorithm="giac")

[Out]

x^3 + 10*x^2 + (x^2 + 15*x)*e^5 - 69*x

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maple [A]  time = 0.03, size = 19, normalized size = 1.12

method	result	size
gosper	\(x \left (x \,{\mathrm e}^{5}+x^{2}+15 \,{\mathrm e}^{5}+10 x -69\right )\)	\(19\)
norman	\(x^{3}+\left ({\mathrm e}^{5}+10\right ) x^{2}+\left (15 \,{\mathrm e}^{5}-69\right ) x\)	\(21\)
default	\({\mathrm e}^{5} \left (x^{2}+15 x \right )+x^{3}+10 x^{2}-69 x\)	\(23\)
risch	\(x^{2} {\mathrm e}^{5}+15 x \,{\mathrm e}^{5}+x^{3}+10 x^{2}-69 x\)	\(24\)

Verification of antiderivative is not currently implemented for this CAS.

[In]

int((2*x+15)*exp(5)+3*x^2+20*x-69,x,method=_RETURNVERBOSE)

[Out]

x*(x*exp(5)+x^2+15*exp(5)+10*x-69)

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maxima [A]  time = 0.36, size = 22, normalized size = 1.29 \begin {gather*} x^{3} + 10 \, x^{2} + {\left (x^{2} + 15 \, x\right )} e^{5} - 69 \, x \end {gather*}

Verification of antiderivative is not currently implemented for this CAS.

[In]

integrate((2*x+15)*exp(5)+3*x^2+20*x-69,x, algorithm="maxima")

[Out]

x^3 + 10*x^2 + (x^2 + 15*x)*e^5 - 69*x

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mupad [B]  time = 0.03, size = 20, normalized size = 1.18 \begin {gather*} x^3+\left ({\mathrm {e}}^5+10\right )\,x^2+\left (15\,{\mathrm {e}}^5-69\right )\,x \end {gather*}

Verification of antiderivative is not currently implemented for this CAS.

[In]

int(20*x + 3*x^2 + exp(5)*(2*x + 15) - 69,x)

[Out]

x^3 + x*(15*exp(5) - 69) + x^2*(exp(5) + 10)

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sympy [A]  time = 0.05, size = 19, normalized size = 1.12 \begin {gather*} x^{3} + x^{2} \left (10 + e^{5}\right ) + x \left (-69 + 15 e^{5}\right ) \end {gather*}

Verification of antiderivative is not currently implemented for this CAS.

[In]

integrate((2*x+15)*exp(5)+3*x**2+20*x-69,x)

[Out]

x**3 + x**2*(10 + exp(5)) + x*(-69 + 15*exp(5))

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