3.76.15 \(\int (-9+10 x) \, dx\)

Optimal. Leaf size=16 \[ x+5 \left (4-2 x+x^2+\log ^2(3)\right ) \]

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Rubi [A]  time = 0.00, antiderivative size = 9, normalized size of antiderivative = 0.56, 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*} 5 x^2-9 x \end {gather*}

Antiderivative was successfully verified.

[In]

Int[-9 + 10*x,x]

[Out]

-9*x + 5*x^2

Rubi steps

\begin {gather*} \begin {aligned} \text {integral} &=-9 x+5 x^2\\ \end {aligned} \end {gather*}

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Mathematica [A]  time = 0.00, size = 9, normalized size = 0.56 \begin {gather*} -9 x+5 x^2 \end {gather*}

Antiderivative was successfully verified.

[In]

Integrate[-9 + 10*x,x]

[Out]

-9*x + 5*x^2

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fricas [A]  time = 0.76, size = 9, normalized size = 0.56 \begin {gather*} 5 \, x^{2} - 9 \, x \end {gather*}

Verification of antiderivative is not currently implemented for this CAS.

[In]

integrate(10*x-9,x, algorithm="fricas")

[Out]

5*x^2 - 9*x

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giac [A]  time = 0.12, size = 9, normalized size = 0.56 \begin {gather*} 5 \, x^{2} - 9 \, x \end {gather*}

Verification of antiderivative is not currently implemented for this CAS.

[In]

integrate(10*x-9,x, algorithm="giac")

[Out]

5*x^2 - 9*x

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maple [A]  time = 0.01, size = 10, normalized size = 0.62

method	result	size
gosper	\(5 x^{2}-9 x\)	\(10\)
default	\(5 x^{2}-9 x\)	\(10\)
norman	\(5 x^{2}-9 x\)	\(10\)
risch	\(5 x^{2}-9 x\)	\(10\)

Verification of antiderivative is not currently implemented for this CAS.

[In]

int(10*x-9,x,method=_RETURNVERBOSE)

[Out]

5*x^2-9*x

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maxima [A]  time = 0.43, size = 9, normalized size = 0.56 \begin {gather*} 5 \, x^{2} - 9 \, x \end {gather*}

Verification of antiderivative is not currently implemented for this CAS.

[In]

integrate(10*x-9,x, algorithm="maxima")

[Out]

5*x^2 - 9*x

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mupad [B]  time = 0.03, size = 7, normalized size = 0.44 \begin {gather*} x\,\left (5\,x-9\right ) \end {gather*}

Verification of antiderivative is not currently implemented for this CAS.

[In]

int(10*x - 9,x)

[Out]

x*(5*x - 9)

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sympy [A]  time = 0.04, size = 7, normalized size = 0.44 \begin {gather*} 5 x^{2} - 9 x \end {gather*}

Verification of antiderivative is not currently implemented for this CAS.

[In]

integrate(10*x-9,x)

[Out]

5*x**2 - 9*x

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