Optimal. Leaf size=27 \[ \frac {a x^{2 n}}{2 n}+\frac {b x^{3 n}}{3 n} \]
[Out]
________________________________________________________________________________________
Rubi [A] time = 0.01, antiderivative size = 27, normalized size of antiderivative = 1.00, number of steps used = 2, number of rules used = 1, integrand size = 15, \(\frac {\text {number of rules}}{\text {integrand size}}\) = 0.067, Rules used = {14} \[ \frac {a x^{2 n}}{2 n}+\frac {b x^{3 n}}{3 n} \]
Antiderivative was successfully verified.
[In]
[Out]
Rule 14
Rubi steps
\begin {align*} \int x^{-1+2 n} \left (a+b x^n\right ) \, dx &=\int \left (a x^{-1+2 n}+b x^{-1+3 n}\right ) \, dx\\ &=\frac {a x^{2 n}}{2 n}+\frac {b x^{3 n}}{3 n}\\ \end {align*}
________________________________________________________________________________________
Mathematica [A] time = 0.01, size = 22, normalized size = 0.81 \[ \frac {x^{2 n} \left (3 a+2 b x^n\right )}{6 n} \]
Antiderivative was successfully verified.
[In]
[Out]
________________________________________________________________________________________
fricas [A] time = 0.50, size = 22, normalized size = 0.81 \[ \frac {2 \, b x^{3 \, n} + 3 \, a x^{2 \, n}}{6 \, n} \]
Verification of antiderivative is not currently implemented for this CAS.
[In]
[Out]
________________________________________________________________________________________
giac [F] time = 0.00, size = 0, normalized size = 0.00 \[ \int {\left (b x^{n} + a\right )} x^{2 \, n - 1}\,{d x} \]
Verification of antiderivative is not currently implemented for this CAS.
[In]
[Out]
________________________________________________________________________________________
maple [A] time = 0.02, size = 28, normalized size = 1.04 \[ \frac {a \,{\mathrm e}^{2 n \ln \relax (x )}}{2 n}+\frac {b \,{\mathrm e}^{3 n \ln \relax (x )}}{3 n} \]
Verification of antiderivative is not currently implemented for this CAS.
[In]
[Out]
________________________________________________________________________________________
maxima [A] time = 0.52, size = 23, normalized size = 0.85 \[ \frac {b x^{3 \, n}}{3 \, n} + \frac {a x^{2 \, n}}{2 \, n} \]
Verification of antiderivative is not currently implemented for this CAS.
[In]
[Out]
________________________________________________________________________________________
mupad [B] time = 1.26, size = 20, normalized size = 0.74 \[ \frac {x^{2\,n}\,\left (3\,a+2\,b\,x^n\right )}{6\,n} \]
Verification of antiderivative is not currently implemented for this CAS.
[In]
[Out]
________________________________________________________________________________________
sympy [A] time = 4.74, size = 26, normalized size = 0.96 \[ \begin {cases} \frac {a x^{2 n}}{2 n} + \frac {b x^{3 n}}{3 n} & \text {for}\: n \neq 0 \\\left (a + b\right ) \log {\relax (x )} & \text {otherwise} \end {cases} \]
Verification of antiderivative is not currently implemented for this CAS.
[In]
[Out]
________________________________________________________________________________________