Optimal. Leaf size=24 \[ -\frac {x^{-9 n} \left (a+b x^n\right )^9}{9 a n} \]
[Out]
________________________________________________________________________________________
Rubi [A]
time = 0.00, antiderivative size = 24, normalized size of antiderivative = 1.00, number of steps
used = 1, number of rules used = 1, integrand size = 17, \(\frac {\text {number of rules}}{\text {integrand size}}\) = 0.059, Rules used = {270}
\begin {gather*} -\frac {x^{-9 n} \left (a+b x^n\right )^9}{9 a n} \end {gather*}
Antiderivative was successfully verified.
[In]
[Out]
Rule 270
Rubi steps
\begin {align*} \int x^{-1-9 n} \left (a+b x^n\right )^8 \, dx &=-\frac {x^{-9 n} \left (a+b x^n\right )^9}{9 a n}\\ \end {align*}
________________________________________________________________________________________
Mathematica [B] Leaf count is larger than twice the leaf count of optimal. \(113\) vs. \(2(24)=48\).
time = 0.02, size = 113, normalized size = 4.71 \begin {gather*} \frac {x^{-9 n} \left (-a^8-9 a^7 b x^n-36 a^6 b^2 x^{2 n}-84 a^5 b^3 x^{3 n}-126 a^4 b^4 x^{4 n}-126 a^3 b^5 x^{5 n}-84 a^2 b^6 x^{6 n}-36 a b^7 x^{7 n}-9 b^8 x^{8 n}\right )}{9 n} \end {gather*}
Antiderivative was successfully verified.
[In]
[Out]
________________________________________________________________________________________
Maple [B] Leaf count of result is larger than twice the leaf count of optimal. \(135\) vs.
\(2(24)=48\).
time = 0.20, size = 136, normalized size = 5.67
method | result | size |
risch | \(-\frac {b^{8} x^{-n}}{n}-\frac {4 a \,b^{7} x^{-2 n}}{n}-\frac {28 a^{2} b^{6} x^{-3 n}}{3 n}-\frac {14 a^{3} b^{5} x^{-4 n}}{n}-\frac {14 a^{4} b^{4} x^{-5 n}}{n}-\frac {28 a^{5} b^{3} x^{-6 n}}{3 n}-\frac {4 a^{6} b^{2} x^{-7 n}}{n}-\frac {a^{7} b \,x^{-8 n}}{n}-\frac {a^{8} x^{-9 n}}{9 n}\) | \(136\) |
Verification of antiderivative is not currently implemented for this CAS.
[In]
[Out]
________________________________________________________________________________________
Maxima [B] Leaf count of result is larger than twice the leaf count of optimal. 151 vs.
\(2 (24) = 48\).
time = 0.29, size = 151, normalized size = 6.29 \begin {gather*} -\frac {a^{8}}{9 \, n x^{9 \, n}} - \frac {a^{7} b}{n x^{8 \, n}} - \frac {4 \, a^{6} b^{2}}{n x^{7 \, n}} - \frac {28 \, a^{5} b^{3}}{3 \, n x^{6 \, n}} - \frac {14 \, a^{4} b^{4}}{n x^{5 \, n}} - \frac {14 \, a^{3} b^{5}}{n x^{4 \, n}} - \frac {28 \, a^{2} b^{6}}{3 \, n x^{3 \, n}} - \frac {4 \, a b^{7}}{n x^{2 \, n}} - \frac {b^{8}}{n x^{n}} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
[In]
[Out]
________________________________________________________________________________________
Fricas [B] Leaf count of result is larger than twice the leaf count of optimal. 111 vs.
\(2 (24) = 48\).
time = 0.38, size = 111, normalized size = 4.62 \begin {gather*} -\frac {9 \, b^{8} x^{8 \, n} + 36 \, a b^{7} x^{7 \, n} + 84 \, a^{2} b^{6} x^{6 \, n} + 126 \, a^{3} b^{5} x^{5 \, n} + 126 \, a^{4} b^{4} x^{4 \, n} + 84 \, a^{5} b^{3} x^{3 \, n} + 36 \, a^{6} b^{2} x^{2 \, n} + 9 \, a^{7} b x^{n} + a^{8}}{9 \, n x^{9 \, n}} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
[In]
[Out]
________________________________________________________________________________________
Sympy [B] Leaf count of result is larger than twice the leaf count of optimal. 134 vs.
\(2 (19) = 38\).
time = 36.95, size = 134, normalized size = 5.58 \begin {gather*} \begin {cases} - \frac {a^{8} x^{- 9 n}}{9 n} - \frac {a^{7} b x^{- 8 n}}{n} - \frac {4 a^{6} b^{2} x^{- 7 n}}{n} - \frac {28 a^{5} b^{3} x^{- 6 n}}{3 n} - \frac {14 a^{4} b^{4} x^{- 5 n}}{n} - \frac {14 a^{3} b^{5} x^{- 4 n}}{n} - \frac {28 a^{2} b^{6} x^{- 3 n}}{3 n} - \frac {4 a b^{7} x^{- 2 n}}{n} - \frac {b^{8} x^{- n}}{n} & \text {for}\: n \neq 0 \\\left (a + b\right )^{8} \log {\left (x \right )} & \text {otherwise} \end {cases} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
[In]
[Out]
________________________________________________________________________________________
Giac [B] Leaf count of result is larger than twice the leaf count of optimal. 111 vs.
\(2 (24) = 48\).
time = 0.62, size = 111, normalized size = 4.62 \begin {gather*} -\frac {9 \, b^{8} x^{8 \, n} + 36 \, a b^{7} x^{7 \, n} + 84 \, a^{2} b^{6} x^{6 \, n} + 126 \, a^{3} b^{5} x^{5 \, n} + 126 \, a^{4} b^{4} x^{4 \, n} + 84 \, a^{5} b^{3} x^{3 \, n} + 36 \, a^{6} b^{2} x^{2 \, n} + 9 \, a^{7} b x^{n} + a^{8}}{9 \, n x^{9 \, n}} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
[In]
[Out]
________________________________________________________________________________________
Mupad [B]
time = 0.00, size = 151, normalized size = 6.29 \begin {gather*} -\frac {a^8}{9\,n\,x^{9\,n}}-\frac {b^8}{n\,x^n}-\frac {28\,a^2\,b^6}{3\,n\,x^{3\,n}}-\frac {14\,a^3\,b^5}{n\,x^{4\,n}}-\frac {14\,a^4\,b^4}{n\,x^{5\,n}}-\frac {28\,a^5\,b^3}{3\,n\,x^{6\,n}}-\frac {4\,a^6\,b^2}{n\,x^{7\,n}}-\frac {4\,a\,b^7}{n\,x^{2\,n}}-\frac {a^7\,b}{n\,x^{8\,n}} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
[In]
[Out]
________________________________________________________________________________________