Optimal. Leaf size=93 \[ -\frac {a^7}{13 x^{13}}-\frac {7 a^6 b}{12 x^{12}}-\frac {21 a^5 b^2}{11 x^{11}}-\frac {7 a^4 b^3}{2 x^{10}}-\frac {35 a^3 b^4}{9 x^9}-\frac {21 a^2 b^5}{8 x^8}-\frac {a b^6}{x^7}-\frac {b^7}{6 x^6} \]
[Out]
________________________________________________________________________________________
Rubi [A] time = 0.03, antiderivative size = 93, normalized size of antiderivative = 1.00, 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} \[ -\frac {21 a^5 b^2}{11 x^{11}}-\frac {7 a^4 b^3}{2 x^{10}}-\frac {35 a^3 b^4}{9 x^9}-\frac {21 a^2 b^5}{8 x^8}-\frac {7 a^6 b}{12 x^{12}}-\frac {a^7}{13 x^{13}}-\frac {a b^6}{x^7}-\frac {b^7}{6 x^6} \]
Antiderivative was successfully verified.
[In]
[Out]
Rule 43
Rubi steps
\begin {align*} \int \frac {(a+b x)^7}{x^{14}} \, dx &=\int \left (\frac {a^7}{x^{14}}+\frac {7 a^6 b}{x^{13}}+\frac {21 a^5 b^2}{x^{12}}+\frac {35 a^4 b^3}{x^{11}}+\frac {35 a^3 b^4}{x^{10}}+\frac {21 a^2 b^5}{x^9}+\frac {7 a b^6}{x^8}+\frac {b^7}{x^7}\right ) \, dx\\ &=-\frac {a^7}{13 x^{13}}-\frac {7 a^6 b}{12 x^{12}}-\frac {21 a^5 b^2}{11 x^{11}}-\frac {7 a^4 b^3}{2 x^{10}}-\frac {35 a^3 b^4}{9 x^9}-\frac {21 a^2 b^5}{8 x^8}-\frac {a b^6}{x^7}-\frac {b^7}{6 x^6}\\ \end {align*}
________________________________________________________________________________________
Mathematica [A] time = 0.01, size = 93, normalized size = 1.00 \[ -\frac {a^7}{13 x^{13}}-\frac {7 a^6 b}{12 x^{12}}-\frac {21 a^5 b^2}{11 x^{11}}-\frac {7 a^4 b^3}{2 x^{10}}-\frac {35 a^3 b^4}{9 x^9}-\frac {21 a^2 b^5}{8 x^8}-\frac {a b^6}{x^7}-\frac {b^7}{6 x^6} \]
Antiderivative was successfully verified.
[In]
[Out]
________________________________________________________________________________________
fricas [A] time = 0.42, size = 79, normalized size = 0.85 \[ -\frac {1716 \, b^{7} x^{7} + 10296 \, a b^{6} x^{6} + 27027 \, a^{2} b^{5} x^{5} + 40040 \, a^{3} b^{4} x^{4} + 36036 \, a^{4} b^{3} x^{3} + 19656 \, a^{5} b^{2} x^{2} + 6006 \, a^{6} b x + 792 \, a^{7}}{10296 \, x^{13}} \]
Verification of antiderivative is not currently implemented for this CAS.
[In]
[Out]
________________________________________________________________________________________
giac [A] time = 1.04, size = 79, normalized size = 0.85 \[ -\frac {1716 \, b^{7} x^{7} + 10296 \, a b^{6} x^{6} + 27027 \, a^{2} b^{5} x^{5} + 40040 \, a^{3} b^{4} x^{4} + 36036 \, a^{4} b^{3} x^{3} + 19656 \, a^{5} b^{2} x^{2} + 6006 \, a^{6} b x + 792 \, a^{7}}{10296 \, x^{13}} \]
Verification of antiderivative is not currently implemented for this CAS.
[In]
[Out]
________________________________________________________________________________________
maple [A] time = 0.00, size = 80, normalized size = 0.86 \[ -\frac {b^{7}}{6 x^{6}}-\frac {a \,b^{6}}{x^{7}}-\frac {21 a^{2} b^{5}}{8 x^{8}}-\frac {35 a^{3} b^{4}}{9 x^{9}}-\frac {7 a^{4} b^{3}}{2 x^{10}}-\frac {21 a^{5} b^{2}}{11 x^{11}}-\frac {7 a^{6} b}{12 x^{12}}-\frac {a^{7}}{13 x^{13}} \]
Verification of antiderivative is not currently implemented for this CAS.
[In]
[Out]
________________________________________________________________________________________
maxima [A] time = 1.37, size = 79, normalized size = 0.85 \[ -\frac {1716 \, b^{7} x^{7} + 10296 \, a b^{6} x^{6} + 27027 \, a^{2} b^{5} x^{5} + 40040 \, a^{3} b^{4} x^{4} + 36036 \, a^{4} b^{3} x^{3} + 19656 \, a^{5} b^{2} x^{2} + 6006 \, a^{6} b x + 792 \, a^{7}}{10296 \, x^{13}} \]
Verification of antiderivative is not currently implemented for this CAS.
[In]
[Out]
________________________________________________________________________________________
mupad [B] time = 0.07, size = 78, normalized size = 0.84 \[ -\frac {\frac {a^7}{13}+\frac {7\,a^6\,b\,x}{12}+\frac {21\,a^5\,b^2\,x^2}{11}+\frac {7\,a^4\,b^3\,x^3}{2}+\frac {35\,a^3\,b^4\,x^4}{9}+\frac {21\,a^2\,b^5\,x^5}{8}+a\,b^6\,x^6+\frac {b^7\,x^7}{6}}{x^{13}} \]
Verification of antiderivative is not currently implemented for this CAS.
[In]
[Out]
________________________________________________________________________________________
sympy [A] time = 0.78, size = 85, normalized size = 0.91 \[ \frac {- 792 a^{7} - 6006 a^{6} b x - 19656 a^{5} b^{2} x^{2} - 36036 a^{4} b^{3} x^{3} - 40040 a^{3} b^{4} x^{4} - 27027 a^{2} b^{5} x^{5} - 10296 a b^{6} x^{6} - 1716 b^{7} x^{7}}{10296 x^{13}} \]
Verification of antiderivative is not currently implemented for this CAS.
[In]
[Out]
________________________________________________________________________________________