3.26.85 \(\int (15+60 x) \, dx\) [2585]

Optimal. Leaf size=25 \[ 5 \left (3-3 \left (-1-e^{\frac {9}{\log (5)}}+(-1-2 x) x\right )\right ) \]

[Out]

30-15*x*(-1-2*x)+15*exp(9/ln(5))

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Rubi [A]
time = 0.00, antiderivative size = 9, normalized size of antiderivative = 0.36, number of steps used = 1, number of rules used = 0, integrand size = 5, \(\frac {\text {number of rules}}{\text {integrand size}}\) = 0.000, Rules used = {} \begin {gather*} 30 x^2+15 x \end {gather*}

Antiderivative was successfully verified.

[In]

Int[15 + 60*x,x]

[Out]

15*x + 30*x^2

Rubi steps

\begin {gather*} \begin {aligned} \text {integral} &=15 x+30 x^2\\ \end {aligned} \end {gather*}

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Mathematica [A]
time = 0.00, size = 9, normalized size = 0.36 \begin {gather*} 15 x+30 x^2 \end {gather*}

Antiderivative was successfully verified.

[In]

Integrate[15 + 60*x,x]

[Out]

15*x + 30*x^2

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Maple [A]
time = 0.08, size = 10, normalized size = 0.40

method	result	size
gosper	\(15 \left (2 x +1\right ) x\)	\(9\)
default	\(30 x^{2}+15 x\)	\(10\)
norman	\(30 x^{2}+15 x\)	\(10\)
risch	\(30 x^{2}+15 x\)	\(10\)

Verification of antiderivative is not currently implemented for this CAS.

[In]

int(60*x+15,x,method=_RETURNVERBOSE)

[Out]

30*x^2+15*x

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Maxima [A]
time = 0.26, size = 9, normalized size = 0.36 \begin {gather*} 30 \, x^{2} + 15 \, x \end {gather*}

Verification of antiderivative is not currently implemented for this CAS.

[In]

integrate(60*x+15,x, algorithm="maxima")

[Out]

30*x^2 + 15*x

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Fricas [A]
time = 0.31, size = 9, normalized size = 0.36 \begin {gather*} 30 \, x^{2} + 15 \, x \end {gather*}

Verification of antiderivative is not currently implemented for this CAS.

[In]

integrate(60*x+15,x, algorithm="fricas")

[Out]

30*x^2 + 15*x

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Sympy [A]
time = 0.01, size = 7, normalized size = 0.28 \begin {gather*} 30 x^{2} + 15 x \end {gather*}

Verification of antiderivative is not currently implemented for this CAS.

[In]

integrate(60*x+15,x)

[Out]

30*x**2 + 15*x

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Giac [A]
time = 0.39, size = 9, normalized size = 0.36 \begin {gather*} 30 \, x^{2} + 15 \, x \end {gather*}

Verification of antiderivative is not currently implemented for this CAS.

[In]

integrate(60*x+15,x, algorithm="giac")

[Out]

30*x^2 + 15*x

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Mupad [B]
time = 0.03, size = 8, normalized size = 0.32 \begin {gather*} 15\,x\,\left (2\,x+1\right ) \end {gather*}

Verification of antiderivative is not currently implemented for this CAS.

[In]

int(60*x + 15,x)

[Out]

15*x*(2*x + 1)

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