Optimal. Leaf size=26 \[ -\frac {a^2}{3 x^3}+2 a b x+\frac {b^2 x^5}{5} \]
[Out]
________________________________________________________________________________________
Rubi [A]
time = 0.01, antiderivative size = 26, normalized size of antiderivative = 1.00, number of steps
used = 2, number of rules used = 1, integrand size = 13, \(\frac {\text {number of rules}}{\text {integrand size}}\) = 0.077, Rules used = {276}
\begin {gather*} -\frac {a^2}{3 x^3}+2 a b x+\frac {b^2 x^5}{5} \end {gather*}
Antiderivative was successfully verified.
[In]
[Out]
Rule 276
Rubi steps
\begin {align*} \int \frac {\left (a+b x^4\right )^2}{x^4} \, dx &=\int \left (2 a b+\frac {a^2}{x^4}+b^2 x^4\right ) \, dx\\ &=-\frac {a^2}{3 x^3}+2 a b x+\frac {b^2 x^5}{5}\\ \end {align*}
________________________________________________________________________________________
Mathematica [A]
time = 0.00, size = 26, normalized size = 1.00 \begin {gather*} -\frac {a^2}{3 x^3}+2 a b x+\frac {b^2 x^5}{5} \end {gather*}
Antiderivative was successfully verified.
[In]
[Out]
________________________________________________________________________________________
Maple [A]
time = 0.12, size = 23, normalized size = 0.88
method | result | size |
default | \(-\frac {a^{2}}{3 x^{3}}+2 a b x +\frac {b^{2} x^{5}}{5}\) | \(23\) |
risch | \(-\frac {a^{2}}{3 x^{3}}+2 a b x +\frac {b^{2} x^{5}}{5}\) | \(23\) |
norman | \(\frac {\frac {1}{5} b^{2} x^{8}+2 a b \,x^{4}-\frac {1}{3} a^{2}}{x^{3}}\) | \(26\) |
gosper | \(-\frac {-3 b^{2} x^{8}-30 a b \,x^{4}+5 a^{2}}{15 x^{3}}\) | \(27\) |
Verification of antiderivative is not currently implemented for this CAS.
[In]
[Out]
________________________________________________________________________________________
Maxima [A]
time = 0.35, size = 22, normalized size = 0.85 \begin {gather*} \frac {1}{5} \, b^{2} x^{5} + 2 \, a b x - \frac {a^{2}}{3 \, x^{3}} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
[In]
[Out]
________________________________________________________________________________________
Fricas [A]
time = 0.36, size = 26, normalized size = 1.00 \begin {gather*} \frac {3 \, b^{2} x^{8} + 30 \, a b x^{4} - 5 \, a^{2}}{15 \, x^{3}} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
[In]
[Out]
________________________________________________________________________________________
Sympy [A]
time = 0.03, size = 22, normalized size = 0.85 \begin {gather*} - \frac {a^{2}}{3 x^{3}} + 2 a b x + \frac {b^{2} x^{5}}{5} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
[In]
[Out]
________________________________________________________________________________________
Giac [A]
time = 0.54, size = 22, normalized size = 0.85 \begin {gather*} \frac {1}{5} \, b^{2} x^{5} + 2 \, a b x - \frac {a^{2}}{3 \, x^{3}} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
[In]
[Out]
________________________________________________________________________________________
Mupad [B]
time = 0.03, size = 22, normalized size = 0.85 \begin {gather*} \frac {b^2\,x^5}{5}-\frac {a^2}{3\,x^3}+2\,a\,b\,x \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
[In]
[Out]
________________________________________________________________________________________