Integrand size = 11, antiderivative size = 19 \[ \int x \left (b x^2\right )^{5/2} \, dx=\frac {1}{7} b^2 x^6 \sqrt {b x^2} \]
[Out]
Time = 0.00 (sec) , antiderivative size = 19, normalized size of antiderivative = 1.00, number of steps used = 2, number of rules used = 2, \(\frac {\text {number of rules}}{\text {integrand size}}\) = 0.182, Rules used = {15, 30} \[ \int x \left (b x^2\right )^{5/2} \, dx=\frac {1}{7} b^2 x^6 \sqrt {b x^2} \]
[In]
[Out]
Rule 15
Rule 30
Rubi steps \begin{align*} \text {integral}& = \frac {\left (b^2 \sqrt {b x^2}\right ) \int x^6 \, dx}{x} \\ & = \frac {1}{7} b^2 x^6 \sqrt {b x^2} \\ \end{align*}
Time = 0.00 (sec) , antiderivative size = 16, normalized size of antiderivative = 0.84 \[ \int x \left (b x^2\right )^{5/2} \, dx=\frac {1}{7} x^2 \left (b x^2\right )^{5/2} \]
[In]
[Out]
Time = 0.08 (sec) , antiderivative size = 13, normalized size of antiderivative = 0.68
method | result | size |
gosper | \(\frac {x^{2} \left (b \,x^{2}\right )^{\frac {5}{2}}}{7}\) | \(13\) |
derivativedivides | \(\frac {\left (b \,x^{2}\right )^{\frac {7}{2}}}{7 b}\) | \(13\) |
default | \(\frac {x^{2} \left (b \,x^{2}\right )^{\frac {5}{2}}}{7}\) | \(13\) |
risch | \(\frac {b^{2} x^{6} \sqrt {b \,x^{2}}}{7}\) | \(16\) |
pseudoelliptic | \(\frac {b^{2} x^{6} \sqrt {b \,x^{2}}}{7}\) | \(16\) |
trager | \(\frac {b^{2} \left (x^{6}+x^{5}+x^{4}+x^{3}+x^{2}+x +1\right ) \left (-1+x \right ) \sqrt {b \,x^{2}}}{7 x}\) | \(37\) |
[In]
[Out]
none
Time = 0.26 (sec) , antiderivative size = 15, normalized size of antiderivative = 0.79 \[ \int x \left (b x^2\right )^{5/2} \, dx=\frac {1}{7} \, \sqrt {b x^{2}} b^{2} x^{6} \]
[In]
[Out]
Time = 0.23 (sec) , antiderivative size = 12, normalized size of antiderivative = 0.63 \[ \int x \left (b x^2\right )^{5/2} \, dx=\frac {x^{2} \left (b x^{2}\right )^{\frac {5}{2}}}{7} \]
[In]
[Out]
none
Time = 0.23 (sec) , antiderivative size = 12, normalized size of antiderivative = 0.63 \[ \int x \left (b x^2\right )^{5/2} \, dx=\frac {\left (b x^{2}\right )^{\frac {7}{2}}}{7 \, b} \]
[In]
[Out]
none
Time = 0.27 (sec) , antiderivative size = 10, normalized size of antiderivative = 0.53 \[ \int x \left (b x^2\right )^{5/2} \, dx=\frac {1}{7} \, b^{\frac {5}{2}} x^{7} \mathrm {sgn}\left (x\right ) \]
[In]
[Out]
Time = 5.74 (sec) , antiderivative size = 10, normalized size of antiderivative = 0.53 \[ \int x \left (b x^2\right )^{5/2} \, dx=\frac {b^{5/2}\,\sqrt {x^{14}}}{7} \]
[In]
[Out]