3.20.15 \(\int (-5 x^{3/2}+7 x^{5/2}) \, dx\) [1915]

Optimal. Leaf size=15 \[ -2 x^{5/2}+2 x^{7/2} \]

[Out]

-2*x^(5/2)+2*x^(7/2)

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Rubi [A]
time = 0.00, antiderivative size = 15, normalized size of antiderivative = 1.00, number of steps used = 1, number of rules used = 0, integrand size = 15, \(\frac {\text {number of rules}}{\text {integrand size}}\) = 0.000, Rules used = {} \begin {gather*} 2 x^{7/2}-2 x^{5/2} \end {gather*}

Antiderivative was successfully verified.

[In]

Int[-5*x^(3/2) + 7*x^(5/2),x]

[Out]

-2*x^(5/2) + 2*x^(7/2)

Rubi steps

\begin {align*} \int \left (-5 x^{3/2}+7 x^{5/2}\right ) \, dx &=-2 x^{5/2}+2 x^{7/2}\\ \end {align*}

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Mathematica [A]
time = 0.01, size = 10, normalized size = 0.67 \begin {gather*} 2 (-1+x) x^{5/2} \end {gather*}

Antiderivative was successfully verified.

[In]

Integrate[-5*x^(3/2) + 7*x^(5/2),x]

[Out]

2*(-1 + x)*x^(5/2)

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Mathics [A]
time = 1.62, size = 8, normalized size = 0.53 \begin {gather*} 2 x^{\frac {5}{2}} \left (-1+x\right ) \end {gather*}

Antiderivative was successfully verified.

[In]

mathics('Integrate[-5*x^(3/2) + 7*x^(5/2),x]')

[Out]

2 x ^ (5 / 2) (-1 + x)

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Maple [A]
time = 0.04, size = 12, normalized size = 0.80

method	result	size
gosper	\(2 x^{\frac {5}{2}} \left (-1+x \right )\)	\(9\)
trager	\(2 x^{\frac {5}{2}} \left (-1+x \right )\)	\(9\)
derivativedivides	\(-2 x^{\frac {5}{2}}+2 x^{\frac {7}{2}}\)	\(12\)
default	\(-2 x^{\frac {5}{2}}+2 x^{\frac {7}{2}}\)	\(12\)
risch	\(-2 x^{\frac {5}{2}}+2 x^{\frac {7}{2}}\)	\(12\)

Verification of antiderivative is not currently implemented for this CAS.

[In]

int(-5*x^(3/2)+7*x^(5/2),x,method=_RETURNVERBOSE)

[Out]

-2*x^(5/2)+2*x^(7/2)

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Maxima [A]
time = 0.28, size = 11, normalized size = 0.73 \begin {gather*} 2 \, x^{\frac {7}{2}} - 2 \, x^{\frac {5}{2}} \end {gather*}

Verification of antiderivative is not currently implemented for this CAS.

[In]

integrate(-5*x^(3/2)+7*x^(5/2),x, algorithm="maxima")

[Out]

2*x^(7/2) - 2*x^(5/2)

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Fricas [A]
time = 0.32, size = 14, normalized size = 0.93 \begin {gather*} 2 \, {\left (x^{3} - x^{2}\right )} \sqrt {x} \end {gather*}

Verification of antiderivative is not currently implemented for this CAS.

[In]

integrate(-5*x^(3/2)+7*x^(5/2),x, algorithm="fricas")

[Out]

2*(x^3 - x^2)*sqrt(x)

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Sympy [A]
time = 0.03, size = 12, normalized size = 0.80 \begin {gather*} 2 x^{\frac {7}{2}} - 2 x^{\frac {5}{2}} \end {gather*}

Verification of antiderivative is not currently implemented for this CAS.

[In]

integrate(-5*x**(3/2)+7*x**(5/2),x)

[Out]

2*x**(7/2) - 2*x**(5/2)

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Giac [A]
time = 0.00, size = 28, normalized size = 1.87 \begin {gather*} -\frac {2}{5}\cdot 5 \sqrt {x} x^{2}+\frac {2}{7}\cdot 7 \sqrt {x} x^{3} \end {gather*}

Verification of antiderivative is not currently implemented for this CAS.

[In]

integrate(-5*x^(3/2)+7*x^(5/2),x)

[Out]

2*x^(7/2) - 2*x^(5/2)

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Mupad [B]
time = 0.03, size = 8, normalized size = 0.53 \begin {gather*} 2\,x^{5/2}\,\left (x-1\right ) \end {gather*}

Verification of antiderivative is not currently implemented for this CAS.

[In]

int(7*x^(5/2) - 5*x^(3/2),x)

[Out]

2*x^(5/2)*(x - 1)

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