Optimal. Leaf size=36 \[ \frac {2}{3} b^2 x^{3/2}+\frac {4}{7} b c x^{7/2}+\frac {2}{11} c^2 x^{11/2} \]
[Out]
________________________________________________________________________________________
Rubi [A]
time = 0.01, antiderivative size = 36, normalized size of antiderivative = 1.00, number of steps
used = 3, number of rules used = 2, integrand size = 19, \(\frac {\text {number of rules}}{\text {integrand size}}\) = 0.105, Rules used = {1598, 276}
\begin {gather*} \frac {2}{3} b^2 x^{3/2}+\frac {4}{7} b c x^{7/2}+\frac {2}{11} c^2 x^{11/2} \end {gather*}
Antiderivative was successfully verified.
[In]
[Out]
Rule 276
Rule 1598
Rubi steps
\begin {align*} \int \frac {\left (b x^2+c x^4\right )^2}{x^{7/2}} \, dx &=\int \sqrt {x} \left (b+c x^2\right )^2 \, dx\\ &=\int \left (b^2 \sqrt {x}+2 b c x^{5/2}+c^2 x^{9/2}\right ) \, dx\\ &=\frac {2}{3} b^2 x^{3/2}+\frac {4}{7} b c x^{7/2}+\frac {2}{11} c^2 x^{11/2}\\ \end {align*}
________________________________________________________________________________________
Mathematica [A]
time = 0.02, size = 30, normalized size = 0.83 \begin {gather*} \frac {2}{231} x^{3/2} \left (77 b^2+66 b c x^2+21 c^2 x^4\right ) \end {gather*}
Antiderivative was successfully verified.
[In]
[Out]
________________________________________________________________________________________
Maple [A]
time = 0.11, size = 25, normalized size = 0.69
method | result | size |
derivativedivides | \(\frac {2 b^{2} x^{\frac {3}{2}}}{3}+\frac {4 b c \,x^{\frac {7}{2}}}{7}+\frac {2 c^{2} x^{\frac {11}{2}}}{11}\) | \(25\) |
default | \(\frac {2 b^{2} x^{\frac {3}{2}}}{3}+\frac {4 b c \,x^{\frac {7}{2}}}{7}+\frac {2 c^{2} x^{\frac {11}{2}}}{11}\) | \(25\) |
gosper | \(\frac {2 x^{\frac {3}{2}} \left (21 c^{2} x^{4}+66 b c \,x^{2}+77 b^{2}\right )}{231}\) | \(27\) |
trager | \(\frac {2 x^{\frac {3}{2}} \left (21 c^{2} x^{4}+66 b c \,x^{2}+77 b^{2}\right )}{231}\) | \(27\) |
risch | \(\frac {2 x^{\frac {3}{2}} \left (21 c^{2} x^{4}+66 b c \,x^{2}+77 b^{2}\right )}{231}\) | \(27\) |
Verification of antiderivative is not currently implemented for this CAS.
[In]
[Out]
________________________________________________________________________________________
Maxima [A]
time = 0.28, size = 24, normalized size = 0.67 \begin {gather*} \frac {2}{11} \, c^{2} x^{\frac {11}{2}} + \frac {4}{7} \, b c x^{\frac {7}{2}} + \frac {2}{3} \, b^{2} x^{\frac {3}{2}} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
[In]
[Out]
________________________________________________________________________________________
Fricas [A]
time = 0.32, size = 27, normalized size = 0.75 \begin {gather*} \frac {2}{231} \, {\left (21 \, c^{2} x^{5} + 66 \, b c x^{3} + 77 \, b^{2} x\right )} \sqrt {x} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
[In]
[Out]
________________________________________________________________________________________
Sympy [A]
time = 0.86, size = 34, normalized size = 0.94 \begin {gather*} \frac {2 b^{2} x^{\frac {3}{2}}}{3} + \frac {4 b c x^{\frac {7}{2}}}{7} + \frac {2 c^{2} x^{\frac {11}{2}}}{11} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
[In]
[Out]
________________________________________________________________________________________
Giac [A]
time = 5.18, size = 24, normalized size = 0.67 \begin {gather*} \frac {2}{11} \, c^{2} x^{\frac {11}{2}} + \frac {4}{7} \, b c x^{\frac {7}{2}} + \frac {2}{3} \, b^{2} x^{\frac {3}{2}} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
[In]
[Out]
________________________________________________________________________________________
Mupad [B]
time = 0.05, size = 26, normalized size = 0.72 \begin {gather*} \frac {2\,x^{3/2}\,\left (77\,b^2+66\,b\,c\,x^2+21\,c^2\,x^4\right )}{231} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
[In]
[Out]
________________________________________________________________________________________