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

Optimal result

Integrand size = 15, antiderivative size = 15 \[ \int \left (-5 x^{3/2}+7 x^{5/2}\right ) \, dx=-2 x^{5/2}+2 x^{7/2} \]

[Out]

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

Rubi [A] (verified)

Time = 0.00 (sec) , antiderivative size = 15, normalized size of antiderivative = 1.00, number of steps used = 1, number of rules used = 0, \(\frac {\text {number of rules}}{\text {integrand size}}\) = 0.000, Rules used = {} \[ \int \left (-5 x^{3/2}+7 x^{5/2}\right ) \, dx=2 x^{7/2}-2 x^{5/2} \]

[In]

Int[-5*x^(3/2) + 7*x^(5/2),x]

[Out]

-2*x^(5/2) + 2*x^(7/2)

Rubi steps \begin{align*} \text {integral}& = -2 x^{5/2}+2 x^{7/2} \\ \end{align*}

Mathematica [A] (verified)

Time = 0.01 (sec) , antiderivative size = 10, normalized size of antiderivative = 0.67 \[ \int \left (-5 x^{3/2}+7 x^{5/2}\right ) \, dx=2 (-1+x) x^{5/2} \]

[In]

Integrate[-5*x^(3/2) + 7*x^(5/2),x]

[Out]

2*(-1 + x)*x^(5/2)

Maple [A] (verified)

Time = 0.04 (sec) , antiderivative size = 9, normalized size of antiderivative = 0.60

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	\(-2 x^{\frac {5}{2}}+2 x^{\frac {7}{2}}\)	\(12\)
parts	\(-2 x^{\frac {5}{2}}+2 x^{\frac {7}{2}}\)	\(12\)

[In]

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

[Out]

2*x^(5/2)*(-1+x)

Fricas [A] (verification not implemented)

none

Time = 0.22 (sec) , antiderivative size = 14, normalized size of antiderivative = 0.93 \[ \int \left (-5 x^{3/2}+7 x^{5/2}\right ) \, dx=2 \, {\left (x^{3} - x^{2}\right )} \sqrt {x} \]

[In]

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

[Out]

2*(x^3 - x^2)*sqrt(x)

Sympy [A] (verification not implemented)

Time = 0.02 (sec) , antiderivative size = 12, normalized size of antiderivative = 0.80 \[ \int \left (-5 x^{3/2}+7 x^{5/2}\right ) \, dx=2 x^{\frac {7}{2}} - 2 x^{\frac {5}{2}} \]

[In]

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

[Out]

2*x**(7/2) - 2*x**(5/2)

Maxima [A] (verification not implemented)

none

Time = 0.21 (sec) , antiderivative size = 11, normalized size of antiderivative = 0.73 \[ \int \left (-5 x^{3/2}+7 x^{5/2}\right ) \, dx=2 \, x^{\frac {7}{2}} - 2 \, x^{\frac {5}{2}} \]

[In]

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

[Out]

2*x^(7/2) - 2*x^(5/2)

Giac [A] (verification not implemented)

none

Time = 0.31 (sec) , antiderivative size = 11, normalized size of antiderivative = 0.73 \[ \int \left (-5 x^{3/2}+7 x^{5/2}\right ) \, dx=2 \, x^{\frac {7}{2}} - 2 \, x^{\frac {5}{2}} \]

[In]

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

[Out]

2*x^(7/2) - 2*x^(5/2)

Mupad [B] (verification not implemented)

Time = 0.03 (sec) , antiderivative size = 8, normalized size of antiderivative = 0.53 \[ \int \left (-5 x^{3/2}+7 x^{5/2}\right ) \, dx=2\,x^{5/2}\,\left (x-1\right ) \]

[In]

int(7*x^(5/2) - 5*x^(3/2),x)

[Out]

2*x^(5/2)*(x - 1)