Optimal. Leaf size=21 \[ x \left (a+b x+c x^2+d x^3\right )^{p+1} \]
[Out]
________________________________________________________________________________________
Rubi [A] time = 0.04, antiderivative size = 21, normalized size of antiderivative = 1.00, number of steps used = 1, number of rules used = 1, integrand size = 46, \(\frac {\text {number of rules}}{\text {integrand size}}\) = 0.022, Rules used = {1588} \[ x \left (a+b x+c x^2+d x^3\right )^{p+1} \]
Antiderivative was successfully verified.
[In]
[Out]
Rule 1588
Rubi steps
\begin {align*} \int \left (a+b x+c x^2+d x^3\right )^p \left (a+b (2+p) x+c (3+2 p) x^2+d (4+3 p) x^3\right ) \, dx &=x \left (a+b x+c x^2+d x^3\right )^{1+p}\\ \end {align*}
________________________________________________________________________________________
Mathematica [A] time = 0.12, size = 19, normalized size = 0.90 \[ x (a+x (b+x (c+d x)))^{p+1} \]
Antiderivative was successfully verified.
[In]
[Out]
________________________________________________________________________________________
fricas [A] time = 0.87, size = 37, normalized size = 1.76 \[ {\left (d x^{4} + c x^{3} + b x^{2} + a x\right )} {\left (d x^{3} + c x^{2} + b x + a\right )}^{p} \]
Verification of antiderivative is not currently implemented for this CAS.
[In]
[Out]
________________________________________________________________________________________
giac [B] time = 1.08, size = 87, normalized size = 4.14 \[ {\left (d x^{3} + c x^{2} + b x + a\right )}^{p} d x^{4} + {\left (d x^{3} + c x^{2} + b x + a\right )}^{p} c x^{3} + {\left (d x^{3} + c x^{2} + b x + a\right )}^{p} b x^{2} + {\left (d x^{3} + c x^{2} + b x + a\right )}^{p} a x \]
Verification of antiderivative is not currently implemented for this CAS.
[In]
[Out]
________________________________________________________________________________________
maple [A] time = 0.00, size = 22, normalized size = 1.05 \[ x \left (d \,x^{3}+c \,x^{2}+b x +a \right )^{p +1} \]
Verification of antiderivative is not currently implemented for this CAS.
[In]
[Out]
________________________________________________________________________________________
maxima [A] time = 0.61, size = 37, normalized size = 1.76 \[ {\left (d x^{4} + c x^{3} + b x^{2} + a x\right )} {\left (d x^{3} + c x^{2} + b x + a\right )}^{p} \]
Verification of antiderivative is not currently implemented for this CAS.
[In]
[Out]
________________________________________________________________________________________
mupad [B] time = 2.27, size = 37, normalized size = 1.76 \[ {\left (d\,x^3+c\,x^2+b\,x+a\right )}^p\,\left (d\,x^4+c\,x^3+b\,x^2+a\,x\right ) \]
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]
________________________________________________________________________________________