Optimal. Leaf size=22 \[ \frac {\left (a+c x^2+d x^3\right )^{n+1}}{n+1} \]
[Out]
________________________________________________________________________________________
Rubi [A] time = 0.02, antiderivative size = 22, normalized size of antiderivative = 1.00, number of steps used = 1, number of rules used = 1, integrand size = 26, \(\frac {\text {number of rules}}{\text {integrand size}}\) = 0.038, Rules used = {1588} \[ \frac {\left (a+c x^2+d x^3\right )^{n+1}}{n+1} \]
Antiderivative was successfully verified.
[In]
[Out]
Rule 1588
Rubi steps
\begin {align*} \int \left (2 c x+3 d x^2\right ) \left (a+c x^2+d x^3\right )^n \, dx &=\frac {\left (a+c x^2+d x^3\right )^{1+n}}{1+n}\\ \end {align*}
________________________________________________________________________________________
Mathematica [A] time = 0.01, size = 21, normalized size = 0.95 \[ \frac {\left (a+x^2 (c+d x)\right )^{n+1}}{n+1} \]
Antiderivative was successfully verified.
[In]
[Out]
________________________________________________________________________________________
fricas [A] time = 0.77, size = 32, normalized size = 1.45 \[ \frac {{\left (d x^{3} + c x^{2} + a\right )} {\left (d x^{3} + c x^{2} + a\right )}^{n}}{n + 1} \]
Verification of antiderivative is not currently implemented for this CAS.
[In]
[Out]
________________________________________________________________________________________
giac [A] time = 0.34, size = 22, normalized size = 1.00 \[ \frac {{\left (d x^{3} + c x^{2} + a\right )}^{n + 1}}{n + 1} \]
Verification of antiderivative is not currently implemented for this CAS.
[In]
[Out]
________________________________________________________________________________________
maple [A] time = 0.00, size = 23, normalized size = 1.05 \[ \frac {\left (d \,x^{3}+c \,x^{2}+a \right )^{n +1}}{n +1} \]
Verification of antiderivative is not currently implemented for this CAS.
[In]
[Out]
________________________________________________________________________________________
maxima [A] time = 0.66, size = 22, normalized size = 1.00 \[ \frac {{\left (d x^{3} + c x^{2} + a\right )}^{n + 1}}{n + 1} \]
Verification of antiderivative is not currently implemented for this CAS.
[In]
[Out]
________________________________________________________________________________________
mupad [B] time = 2.14, size = 43, normalized size = 1.95 \[ \left (\frac {a}{n+1}+\frac {c\,x^2}{n+1}+\frac {d\,x^3}{n+1}\right )\,{\left (d\,x^3+c\,x^2+a\right )}^n \]
Verification of antiderivative is not currently implemented for this CAS.
[In]
[Out]
________________________________________________________________________________________
sympy [F(-1)] time = 0.00, size = 0, normalized size = 0.00 \[ \text {Timed out} \]
Verification of antiderivative is not currently implemented for this CAS.
[In]
[Out]
________________________________________________________________________________________