3.63.22 \(\int -\frac {18 x}{25} \, dx\)

Optimal. Leaf size=16 \[ 5+25 e^{-32+e}-\frac {9 x^2}{25} \]

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Rubi [A]  time = 0.00, antiderivative size = 7, normalized size of antiderivative = 0.44, number of steps used = 2, number of rules used = 2, integrand size = 5, \(\frac {\text {number of rules}}{\text {integrand size}}\) = 0.400, Rules used = {12, 30} \begin {gather*} -\frac {9 x^2}{25} \end {gather*}

Antiderivative was successfully verified.

[In]

Int[(-18*x)/25,x]

[Out]

(-9*x^2)/25

Rule 12

Int[(a_)*(u_), x_Symbol] :> Dist[a, Int[u, x], x] /; FreeQ[a, x] &&  !MatchQ[u, (b_)*(v_) /; FreeQ[b, x]]

Rule 30

Int[(x_)^(m_.), x_Symbol] :> Simp[x^(m + 1)/(m + 1), x] /; FreeQ[m, x] && NeQ[m, -1]

Rubi steps

\begin {gather*} \begin {aligned} \text {integral} &=-\frac {18 \int x \, dx}{25}\\ &=-\frac {9 x^2}{25}\\ \end {aligned} \end {gather*}

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Mathematica [A]  time = 0.00, size = 7, normalized size = 0.44 \begin {gather*} -\frac {9 x^2}{25} \end {gather*}

Antiderivative was successfully verified.

[In]

Integrate[(-18*x)/25,x]

[Out]

(-9*x^2)/25

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fricas [A]  time = 0.74, size = 5, normalized size = 0.31 \begin {gather*} -\frac {9}{25} \, x^{2} \end {gather*}

Verification of antiderivative is not currently implemented for this CAS.

[In]

integrate(-18/25*x,x, algorithm="fricas")

[Out]

-9/25*x^2

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giac [A]  time = 0.21, size = 5, normalized size = 0.31 \begin {gather*} -\frac {9}{25} \, x^{2} \end {gather*}

Verification of antiderivative is not currently implemented for this CAS.

[In]

integrate(-18/25*x,x, algorithm="giac")

[Out]

-9/25*x^2

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maple [A]  time = 0.01, size = 6, normalized size = 0.38

method	result	size
gosper	\(-\frac {9 x^{2}}{25}\)	\(6\)
default	\(-\frac {9 x^{2}}{25}\)	\(6\)
norman	\(-\frac {9 x^{2}}{25}\)	\(6\)
risch	\(-\frac {9 x^{2}}{25}\)	\(6\)

Verification of antiderivative is not currently implemented for this CAS.

[In]

int(-18/25*x,x,method=_RETURNVERBOSE)

[Out]

-9/25*x^2

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maxima [A]  time = 0.37, size = 5, normalized size = 0.31 \begin {gather*} -\frac {9}{25} \, x^{2} \end {gather*}

Verification of antiderivative is not currently implemented for this CAS.

[In]

integrate(-18/25*x,x, algorithm="maxima")

[Out]

-9/25*x^2

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mupad [B]  time = 0.01, size = 5, normalized size = 0.31 \begin {gather*} -\frac {9\,x^2}{25} \end {gather*}

Verification of antiderivative is not currently implemented for this CAS.

[In]

int(-(18*x)/25,x)

[Out]

-(9*x^2)/25

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sympy [A]  time = 0.01, size = 7, normalized size = 0.44 \begin {gather*} - \frac {9 x^{2}}{25} \end {gather*}

Verification of antiderivative is not currently implemented for this CAS.

[In]

integrate(-18/25*x,x)

[Out]

-9*x**2/25

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