Optimal. Leaf size=27 \[ \frac{\left (a+b x^{5 m+1}\right )^6}{6 b (5 m+1)} \]
[Out]
________________________________________________________________________________________
Rubi [A] time = 0.0102364, antiderivative size = 27, normalized size of antiderivative = 1., number of steps used = 2, number of rules used = 2, integrand size = 17, \(\frac{\text{number of rules}}{\text{integrand size}}\) = 0.118, Rules used = {1593, 261} \[ \frac{\left (a+b x^{5 m+1}\right )^6}{6 b (5 m+1)} \]
Antiderivative was successfully verified.
[In]
[Out]
Rule 1593
Rule 261
Rubi steps
\begin{align*} \int \left (a x^m+b x^{1+6 m}\right )^5 \, dx &=\int x^{5 m} \left (a+b x^{1+5 m}\right )^5 \, dx\\ &=\frac{\left (a+b x^{1+5 m}\right )^6}{6 b (1+5 m)}\\ \end{align*}
Mathematica [A] time = 0.0133221, size = 27, normalized size = 1. \[ \frac{\left (a+b x^{5 m+1}\right )^6}{6 b (5 m+1)} \]
Antiderivative was successfully verified.
[In]
[Out]
________________________________________________________________________________________
Maple [B] time = 0.018, size = 126, normalized size = 4.7 \begin{align*}{\frac{{b}^{5}{x}^{6} \left ({x}^{m} \right ) ^{30}}{6+30\,m}}+{\frac{a{b}^{4}{x}^{5} \left ({x}^{m} \right ) ^{25}}{1+5\,m}}+{\frac{5\,{a}^{2}{b}^{3}{x}^{4} \left ({x}^{m} \right ) ^{20}}{2+10\,m}}+{\frac{10\,{a}^{3}{b}^{2}{x}^{3} \left ({x}^{m} \right ) ^{15}}{3+15\,m}}+{\frac{5\,{a}^{4}b{x}^{2} \left ({x}^{m} \right ) ^{10}}{2+10\,m}}+{\frac{{a}^{5}x \left ({x}^{m} \right ) ^{5}}{1+5\,m}} \end{align*}
Verification of antiderivative is not currently implemented for this CAS.
[In]
[Out]
________________________________________________________________________________________
Maxima [F(-2)] time = 0., size = 0, normalized size = 0. \begin{align*} \text{Exception raised: ValueError} \end{align*}
Verification of antiderivative is not currently implemented for this CAS.
[In]
[Out]
________________________________________________________________________________________
Fricas [B] time = 0.85108, size = 204, normalized size = 7.56 \begin{align*} \frac{b^{5} x^{6} x^{30 \, m} + 6 \, a b^{4} x^{5} x^{25 \, m} + 15 \, a^{2} b^{3} x^{4} x^{20 \, m} + 20 \, a^{3} b^{2} x^{3} x^{15 \, m} + 15 \, a^{4} b x^{2} x^{10 \, m} + 6 \, a^{5} x x^{5 \, m}}{6 \,{\left (5 \, m + 1\right )}} \end{align*}
Verification of antiderivative is not currently implemented for this CAS.
[In]
[Out]
________________________________________________________________________________________
Sympy [F(-1)] time = 0., size = 0, normalized size = 0. \begin{align*} \text{Timed out} \end{align*}
Verification of antiderivative is not currently implemented for this CAS.
[In]
[Out]
________________________________________________________________________________________
Giac [B] time = 1.12316, size = 126, normalized size = 4.67 \begin{align*} \frac{b^{5} x^{6} x^{30 \, m} + 6 \, a b^{4} x^{5} x^{25 \, m} + 15 \, a^{2} b^{3} x^{4} x^{20 \, m} + 20 \, a^{3} b^{2} x^{3} x^{15 \, m} + 15 \, a^{4} b x^{2} x^{10 \, m} + 6 \, a^{5} x x^{5 \, m}}{6 \,{\left (5 \, m + 1\right )}} \end{align*}
Verification of antiderivative is not currently implemented for this CAS.
[In]
[Out]