Optimal. Leaf size=15 \[ -\frac{1}{7 \left (b x+c x^2\right )^7} \]
[Out]
________________________________________________________________________________________
Rubi [A] time = 0.0039839, antiderivative size = 15, normalized size of antiderivative = 1., number of steps used = 1, number of rules used = 1, integrand size = 18, \(\frac{\text{number of rules}}{\text{integrand size}}\) = 0.056, Rules used = {629} \[ -\frac{1}{7 \left (b x+c x^2\right )^7} \]
Antiderivative was successfully verified.
[In]
[Out]
Rule 629
Rubi steps
\begin{align*} \int \frac{b+2 c x}{\left (b x+c x^2\right )^8} \, dx &=-\frac{1}{7 \left (b x+c x^2\right )^7}\\ \end{align*}
Mathematica [A] time = 0.021585, size = 14, normalized size = 0.93 \[ -\frac{1}{7 x^7 (b+c x)^7} \]
Antiderivative was successfully verified.
[In]
[Out]
________________________________________________________________________________________
Maple [B] time = 0., size = 177, normalized size = 11.8 \begin{align*} -{\frac{1}{7\,{b}^{7}{x}^{7}}}-132\,{\frac{{c}^{6}}{{b}^{13}x}}+66\,{\frac{{c}^{5}}{{b}^{12}{x}^{2}}}-30\,{\frac{{c}^{4}}{{b}^{11}{x}^{3}}}+12\,{\frac{{c}^{3}}{{b}^{10}{x}^{4}}}-4\,{\frac{{c}^{2}}{{b}^{9}{x}^{5}}}+{\frac{c}{{b}^{8}{x}^{6}}}+132\,{\frac{{c}^{7}}{{b}^{13} \left ( cx+b \right ) }}+66\,{\frac{{c}^{7}}{{b}^{12} \left ( cx+b \right ) ^{2}}}+30\,{\frac{{c}^{7}}{{b}^{11} \left ( cx+b \right ) ^{3}}}+12\,{\frac{{c}^{7}}{{b}^{10} \left ( cx+b \right ) ^{4}}}+4\,{\frac{{c}^{7}}{{b}^{9} \left ( cx+b \right ) ^{5}}}+{\frac{{c}^{7}}{{b}^{8} \left ( cx+b \right ) ^{6}}}+{\frac{{c}^{7}}{7\,{b}^{7} \left ( cx+b \right ) ^{7}}} \end{align*}
Verification of antiderivative is not currently implemented for this CAS.
[In]
[Out]
________________________________________________________________________________________
Maxima [A] time = 1.07506, size = 18, normalized size = 1.2 \begin{align*} -\frac{1}{7 \,{\left (c x^{2} + b x\right )}^{7}} \end{align*}
Verification of antiderivative is not currently implemented for this CAS.
[In]
[Out]
________________________________________________________________________________________
Fricas [B] time = 1.35239, size = 171, normalized size = 11.4 \begin{align*} -\frac{1}{7 \,{\left (c^{7} x^{14} + 7 \, b c^{6} x^{13} + 21 \, b^{2} c^{5} x^{12} + 35 \, b^{3} c^{4} x^{11} + 35 \, b^{4} c^{3} x^{10} + 21 \, b^{5} c^{2} x^{9} + 7 \, b^{6} c x^{8} + b^{7} x^{7}\right )}} \end{align*}
Verification of antiderivative is not currently implemented for this CAS.
[In]
[Out]
________________________________________________________________________________________
Sympy [B] time = 3.97716, size = 87, normalized size = 5.8 \begin{align*} - \frac{1}{7 b^{7} x^{7} + 49 b^{6} c x^{8} + 147 b^{5} c^{2} x^{9} + 245 b^{4} c^{3} x^{10} + 245 b^{3} c^{4} x^{11} + 147 b^{2} c^{5} x^{12} + 49 b c^{6} x^{13} + 7 c^{7} x^{14}} \end{align*}
Verification of antiderivative is not currently implemented for this CAS.
[In]
[Out]
________________________________________________________________________________________
Giac [A] time = 1.23788, size = 18, normalized size = 1.2 \begin{align*} -\frac{1}{7 \,{\left (c x^{2} + b x\right )}^{7}} \end{align*}
Verification of antiderivative is not currently implemented for this CAS.
[In]
[Out]