Optimal. Leaf size=150 \[ \frac{14 a^2 x^2}{b^9}-\frac{a^{10}}{6 b^{11} (a+b x)^6}+\frac{2 a^9}{b^{11} (a+b x)^5}-\frac{45 a^8}{4 b^{11} (a+b x)^4}+\frac{40 a^7}{b^{11} (a+b x)^3}-\frac{105 a^6}{b^{11} (a+b x)^2}+\frac{252 a^5}{b^{11} (a+b x)}-\frac{84 a^3 x}{b^{10}}+\frac{210 a^4 \log (a+b x)}{b^{11}}-\frac{7 a x^3}{3 b^8}+\frac{x^4}{4 b^7} \]
[Out]
________________________________________________________________________________________
Rubi [A] time = 0.13534, antiderivative size = 150, normalized size of antiderivative = 1., number of steps used = 2, number of rules used = 1, integrand size = 11, \(\frac{\text{number of rules}}{\text{integrand size}}\) = 0.091, Rules used = {43} \[ \frac{14 a^2 x^2}{b^9}-\frac{a^{10}}{6 b^{11} (a+b x)^6}+\frac{2 a^9}{b^{11} (a+b x)^5}-\frac{45 a^8}{4 b^{11} (a+b x)^4}+\frac{40 a^7}{b^{11} (a+b x)^3}-\frac{105 a^6}{b^{11} (a+b x)^2}+\frac{252 a^5}{b^{11} (a+b x)}-\frac{84 a^3 x}{b^{10}}+\frac{210 a^4 \log (a+b x)}{b^{11}}-\frac{7 a x^3}{3 b^8}+\frac{x^4}{4 b^7} \]
Antiderivative was successfully verified.
[In]
[Out]
Rule 43
Rubi steps
\begin{align*} \int \frac{x^{10}}{(a+b x)^7} \, dx &=\int \left (-\frac{84 a^3}{b^{10}}+\frac{28 a^2 x}{b^9}-\frac{7 a x^2}{b^8}+\frac{x^3}{b^7}+\frac{a^{10}}{b^{10} (a+b x)^7}-\frac{10 a^9}{b^{10} (a+b x)^6}+\frac{45 a^8}{b^{10} (a+b x)^5}-\frac{120 a^7}{b^{10} (a+b x)^4}+\frac{210 a^6}{b^{10} (a+b x)^3}-\frac{252 a^5}{b^{10} (a+b x)^2}+\frac{210 a^4}{b^{10} (a+b x)}\right ) \, dx\\ &=-\frac{84 a^3 x}{b^{10}}+\frac{14 a^2 x^2}{b^9}-\frac{7 a x^3}{3 b^8}+\frac{x^4}{4 b^7}-\frac{a^{10}}{6 b^{11} (a+b x)^6}+\frac{2 a^9}{b^{11} (a+b x)^5}-\frac{45 a^8}{4 b^{11} (a+b x)^4}+\frac{40 a^7}{b^{11} (a+b x)^3}-\frac{105 a^6}{b^{11} (a+b x)^2}+\frac{252 a^5}{b^{11} (a+b x)}+\frac{210 a^4 \log (a+b x)}{b^{11}}\\ \end{align*}
Mathematica [A] time = 0.0355748, size = 139, normalized size = 0.93 \[ \frac{18105 a^8 b^2 x^2+11540 a^7 b^3 x^3-3945 a^6 b^4 x^4-9138 a^5 b^5 x^5-4043 a^4 b^6 x^6-360 a^3 b^7 x^7+45 a^2 b^8 x^8+10266 a^9 b x+2520 a^4 (a+b x)^6 \log (a+b x)+2131 a^{10}-10 a b^9 x^9+3 b^{10} x^{10}}{12 b^{11} (a+b x)^6} \]
Antiderivative was successfully verified.
[In]
[Out]
________________________________________________________________________________________
Maple [A] time = 0.012, size = 143, normalized size = 1. \begin{align*} -84\,{\frac{{a}^{3}x}{{b}^{10}}}+14\,{\frac{{a}^{2}{x}^{2}}{{b}^{9}}}-{\frac{7\,a{x}^{3}}{3\,{b}^{8}}}+{\frac{{x}^{4}}{4\,{b}^{7}}}-{\frac{{a}^{10}}{6\,{b}^{11} \left ( bx+a \right ) ^{6}}}+2\,{\frac{{a}^{9}}{{b}^{11} \left ( bx+a \right ) ^{5}}}-{\frac{45\,{a}^{8}}{4\,{b}^{11} \left ( bx+a \right ) ^{4}}}+40\,{\frac{{a}^{7}}{{b}^{11} \left ( bx+a \right ) ^{3}}}-105\,{\frac{{a}^{6}}{{b}^{11} \left ( bx+a \right ) ^{2}}}+252\,{\frac{{a}^{5}}{{b}^{11} \left ( bx+a \right ) }}+210\,{\frac{{a}^{4}\ln \left ( bx+a \right ) }{{b}^{11}}} \end{align*}
Verification of antiderivative is not currently implemented for this CAS.
[In]
[Out]
________________________________________________________________________________________
Maxima [A] time = 1.08163, size = 243, normalized size = 1.62 \begin{align*} \frac{3024 \, a^{5} b^{5} x^{5} + 13860 \, a^{6} b^{4} x^{4} + 25680 \, a^{7} b^{3} x^{3} + 23985 \, a^{8} b^{2} x^{2} + 11274 \, a^{9} b x + 2131 \, a^{10}}{12 \,{\left (b^{17} x^{6} + 6 \, a b^{16} x^{5} + 15 \, a^{2} b^{15} x^{4} + 20 \, a^{3} b^{14} x^{3} + 15 \, a^{4} b^{13} x^{2} + 6 \, a^{5} b^{12} x + a^{6} b^{11}\right )}} + \frac{210 \, a^{4} \log \left (b x + a\right )}{b^{11}} + \frac{3 \, b^{3} x^{4} - 28 \, a b^{2} x^{3} + 168 \, a^{2} b x^{2} - 1008 \, a^{3} x}{12 \, b^{10}} \end{align*}
Verification of antiderivative is not currently implemented for this CAS.
[In]
[Out]
________________________________________________________________________________________
Fricas [A] time = 1.45993, size = 568, normalized size = 3.79 \begin{align*} \frac{3 \, b^{10} x^{10} - 10 \, a b^{9} x^{9} + 45 \, a^{2} b^{8} x^{8} - 360 \, a^{3} b^{7} x^{7} - 4043 \, a^{4} b^{6} x^{6} - 9138 \, a^{5} b^{5} x^{5} - 3945 \, a^{6} b^{4} x^{4} + 11540 \, a^{7} b^{3} x^{3} + 18105 \, a^{8} b^{2} x^{2} + 10266 \, a^{9} b x + 2131 \, a^{10} + 2520 \,{\left (a^{4} b^{6} x^{6} + 6 \, a^{5} b^{5} x^{5} + 15 \, a^{6} b^{4} x^{4} + 20 \, a^{7} b^{3} x^{3} + 15 \, a^{8} b^{2} x^{2} + 6 \, a^{9} b x + a^{10}\right )} \log \left (b x + a\right )}{12 \,{\left (b^{17} x^{6} + 6 \, a b^{16} x^{5} + 15 \, a^{2} b^{15} x^{4} + 20 \, a^{3} b^{14} x^{3} + 15 \, a^{4} b^{13} x^{2} + 6 \, a^{5} b^{12} x + a^{6} b^{11}\right )}} \end{align*}
Verification of antiderivative is not currently implemented for this CAS.
[In]
[Out]
________________________________________________________________________________________
Sympy [A] time = 1.40053, size = 190, normalized size = 1.27 \begin{align*} \frac{210 a^{4} \log{\left (a + b x \right )}}{b^{11}} - \frac{84 a^{3} x}{b^{10}} + \frac{14 a^{2} x^{2}}{b^{9}} - \frac{7 a x^{3}}{3 b^{8}} + \frac{2131 a^{10} + 11274 a^{9} b x + 23985 a^{8} b^{2} x^{2} + 25680 a^{7} b^{3} x^{3} + 13860 a^{6} b^{4} x^{4} + 3024 a^{5} b^{5} x^{5}}{12 a^{6} b^{11} + 72 a^{5} b^{12} x + 180 a^{4} b^{13} x^{2} + 240 a^{3} b^{14} x^{3} + 180 a^{2} b^{15} x^{4} + 72 a b^{16} x^{5} + 12 b^{17} x^{6}} + \frac{x^{4}}{4 b^{7}} \end{align*}
Verification of antiderivative is not currently implemented for this CAS.
[In]
[Out]
________________________________________________________________________________________
Giac [A] time = 1.18732, size = 173, normalized size = 1.15 \begin{align*} \frac{210 \, a^{4} \log \left ({\left | b x + a \right |}\right )}{b^{11}} + \frac{3024 \, a^{5} b^{5} x^{5} + 13860 \, a^{6} b^{4} x^{4} + 25680 \, a^{7} b^{3} x^{3} + 23985 \, a^{8} b^{2} x^{2} + 11274 \, a^{9} b x + 2131 \, a^{10}}{12 \,{\left (b x + a\right )}^{6} b^{11}} + \frac{3 \, b^{21} x^{4} - 28 \, a b^{20} x^{3} + 168 \, a^{2} b^{19} x^{2} - 1008 \, a^{3} b^{18} x}{12 \, b^{28}} \end{align*}
Verification of antiderivative is not currently implemented for this CAS.
[In]
[Out]