Optimal. Leaf size=53 \[ -\frac {a^3 \log \left (a+b x^5\right )}{5 b^4}+\frac {a^2 x^5}{5 b^3}-\frac {a x^{10}}{10 b^2}+\frac {x^{15}}{15 b} \]
[Out]
________________________________________________________________________________________
Rubi [A] time = 0.03, antiderivative size = 53, normalized size of antiderivative = 1.00, number of steps used = 3, number of rules used = 2, integrand size = 13, \(\frac {\text {number of rules}}{\text {integrand size}}\) = 0.154, Rules used = {266, 43} \[ \frac {a^2 x^5}{5 b^3}-\frac {a^3 \log \left (a+b x^5\right )}{5 b^4}-\frac {a x^{10}}{10 b^2}+\frac {x^{15}}{15 b} \]
Antiderivative was successfully verified.
[In]
[Out]
Rule 43
Rule 266
Rubi steps
\begin {align*} \int \frac {x^{19}}{a+b x^5} \, dx &=\frac {1}{5} \operatorname {Subst}\left (\int \frac {x^3}{a+b x} \, dx,x,x^5\right )\\ &=\frac {1}{5} \operatorname {Subst}\left (\int \left (\frac {a^2}{b^3}-\frac {a x}{b^2}+\frac {x^2}{b}-\frac {a^3}{b^3 (a+b x)}\right ) \, dx,x,x^5\right )\\ &=\frac {a^2 x^5}{5 b^3}-\frac {a x^{10}}{10 b^2}+\frac {x^{15}}{15 b}-\frac {a^3 \log \left (a+b x^5\right )}{5 b^4}\\ \end {align*}
________________________________________________________________________________________
Mathematica [A] time = 0.01, size = 53, normalized size = 1.00 \[ -\frac {a^3 \log \left (a+b x^5\right )}{5 b^4}+\frac {a^2 x^5}{5 b^3}-\frac {a x^{10}}{10 b^2}+\frac {x^{15}}{15 b} \]
Antiderivative was successfully verified.
[In]
[Out]
________________________________________________________________________________________
fricas [A] time = 0.60, size = 45, normalized size = 0.85 \[ \frac {2 \, b^{3} x^{15} - 3 \, a b^{2} x^{10} + 6 \, a^{2} b x^{5} - 6 \, a^{3} \log \left (b x^{5} + a\right )}{30 \, b^{4}} \]
Verification of antiderivative is not currently implemented for this CAS.
[In]
[Out]
________________________________________________________________________________________
giac [A] time = 0.21, size = 47, normalized size = 0.89 \[ -\frac {a^{3} \log \left ({\left | b x^{5} + a \right |}\right )}{5 \, b^{4}} + \frac {2 \, b^{2} x^{15} - 3 \, a b x^{10} + 6 \, a^{2} x^{5}}{30 \, b^{3}} \]
Verification of antiderivative is not currently implemented for this CAS.
[In]
[Out]
________________________________________________________________________________________
maple [A] time = 0.00, size = 46, normalized size = 0.87 \[ \frac {x^{15}}{15 b}-\frac {a \,x^{10}}{10 b^{2}}+\frac {a^{2} x^{5}}{5 b^{3}}-\frac {a^{3} \ln \left (b \,x^{5}+a \right )}{5 b^{4}} \]
Verification of antiderivative is not currently implemented for this CAS.
[In]
[Out]
________________________________________________________________________________________
maxima [A] time = 1.01, size = 46, normalized size = 0.87 \[ -\frac {a^{3} \log \left (b x^{5} + a\right )}{5 \, b^{4}} + \frac {2 \, b^{2} x^{15} - 3 \, a b x^{10} + 6 \, a^{2} x^{5}}{30 \, b^{3}} \]
Verification of antiderivative is not currently implemented for this CAS.
[In]
[Out]
________________________________________________________________________________________
mupad [B] time = 0.05, size = 45, normalized size = 0.85 \[ \frac {x^{15}}{15\,b}-\frac {a\,x^{10}}{10\,b^2}-\frac {a^3\,\ln \left (b\,x^5+a\right )}{5\,b^4}+\frac {a^2\,x^5}{5\,b^3} \]
Verification of antiderivative is not currently implemented for this CAS.
[In]
[Out]
________________________________________________________________________________________
sympy [A] time = 0.67, size = 44, normalized size = 0.83 \[ - \frac {a^{3} \log {\left (a + b x^{5} \right )}}{5 b^{4}} + \frac {a^{2} x^{5}}{5 b^{3}} - \frac {a x^{10}}{10 b^{2}} + \frac {x^{15}}{15 b} \]
Verification of antiderivative is not currently implemented for this CAS.
[In]
[Out]
________________________________________________________________________________________