Optimal. Leaf size=21 \[ \frac {\left (c x^2+d x^3\right )^{n+1}}{n+1} \]
[Out]
________________________________________________________________________________________
Rubi [A] time = 0.01, antiderivative size = 21, normalized size of antiderivative = 1.00, number of steps used = 1, number of rules used = 1, integrand size = 23, \(\frac {\text {number of rules}}{\text {integrand size}}\) = 0.043, Rules used = {1588} \[ \frac {\left (c x^2+d x^3\right )^{n+1}}{n+1} \]
Antiderivative was successfully verified.
[In]
[Out]
Rule 1588
Rubi steps
\begin {align*} \int x (2 c+3 d x) \left (c x^2+d x^3\right )^n \, dx &=\frac {\left (c x^2+d x^3\right )^{1+n}}{1+n}\\ \end {align*}
________________________________________________________________________________________
Mathematica [A] time = 0.00, size = 19, normalized size = 0.90 \[ \frac {\left (x^2 (c+d x)\right )^{n+1}}{n+1} \]
Antiderivative was successfully verified.
[In]
[Out]
________________________________________________________________________________________
fricas [A] time = 0.76, size = 30, normalized size = 1.43 \[ \frac {{\left (d x^{3} + c x^{2}\right )} {\left (d x^{3} + c x^{2}\right )}^{n}}{n + 1} \]
Verification of antiderivative is not currently implemented for this CAS.
[In]
[Out]
________________________________________________________________________________________
giac [A] time = 0.40, size = 21, normalized size = 1.00 \[ \frac {{\left (d x^{3} + c x^{2}\right )}^{n + 1}}{n + 1} \]
Verification of antiderivative is not currently implemented for this CAS.
[In]
[Out]
________________________________________________________________________________________
maple [A] time = 0.00, size = 28, normalized size = 1.33 \[ \frac {\left (d x +c \right ) x^{2} \left (d \,x^{3}+c \,x^{2}\right )^{n}}{n +1} \]
Verification of antiderivative is not currently implemented for this CAS.
[In]
[Out]
________________________________________________________________________________________
maxima [A] time = 0.93, size = 32, normalized size = 1.52 \[ \frac {{\left (d x^{3} + c x^{2}\right )} e^{\left (n \log \left (d x + c\right ) + 2 \, n \log \relax (x)\right )}}{n + 1} \]
Verification of antiderivative is not currently implemented for this CAS.
[In]
[Out]
________________________________________________________________________________________
mupad [B] time = 2.15, size = 27, normalized size = 1.29 \[ \frac {x^2\,{\left (d\,x^3+c\,x^2\right )}^n\,\left (c+d\,x\right )}{n+1} \]
Verification of antiderivative is not currently implemented for this CAS.
[In]
[Out]
________________________________________________________________________________________
sympy [A] time = 1.14, size = 53, normalized size = 2.52 \[ \begin {cases} \frac {c x^{2} \left (c x^{2} + d x^{3}\right )^{n}}{n + 1} + \frac {d x^{3} \left (c x^{2} + d x^{3}\right )^{n}}{n + 1} & \text {for}\: n \neq -1 \\2 \log {\relax (x )} + \log {\left (\frac {c}{d} + x \right )} & \text {otherwise} \end {cases} \]
Verification of antiderivative is not currently implemented for this CAS.
[In]
[Out]
________________________________________________________________________________________