Optimal. Leaf size=23 \[ \frac {\left (a+b x+c x^2+d x^3\right )^{p+1}}{x^2} \]
[Out]
________________________________________________________________________________________
Rubi [A] time = 0.04, antiderivative size = 23, normalized size of antiderivative = 1.00, number of steps used = 1, number of rules used = 1, integrand size = 48, \(\frac {\text {number of rules}}{\text {integrand size}}\) = 0.021, Rules used = {1590} \[ \frac {\left (a+b x+c x^2+d x^3\right )^{p+1}}{x^2} \]
Antiderivative was successfully verified.
[In]
[Out]
Rule 1590
Rubi steps
\begin {align*} \int \frac {\left (a+b x+c x^2+d x^3\right )^p \left (-2 a+b (-1+p) x+2 c p x^2+d (1+3 p) x^3\right )}{x^3} \, dx &=\frac {\left (a+b x+c x^2+d x^3\right )^{1+p}}{x^2}\\ \end {align*}
________________________________________________________________________________________
Mathematica [A] time = 0.20, size = 21, normalized size = 0.91 \[ \frac {(a+x (b+x (c+d x)))^{p+1}}{x^2} \]
Antiderivative was successfully verified.
[In]
[Out]
________________________________________________________________________________________
fricas [A] time = 1.04, size = 36, normalized size = 1.57 \[ \frac {{\left (d x^{3} + c x^{2} + b x + a\right )} {\left (d x^{3} + c x^{2} + b x + a\right )}^{p}}{x^{2}} \]
Verification of antiderivative is not currently implemented for this CAS.
[In]
[Out]
________________________________________________________________________________________
giac [F] time = 0.00, size = 0, normalized size = 0.00 \[ \int \frac {{\left (d {\left (3 \, p + 1\right )} x^{3} + 2 \, c p x^{2} + b {\left (p - 1\right )} x - 2 \, a\right )} {\left (d x^{3} + c x^{2} + b x + a\right )}^{p}}{x^{3}}\,{d x} \]
Verification of antiderivative is not currently implemented for this CAS.
[In]
[Out]
________________________________________________________________________________________
maple [A] time = 0.01, size = 24, normalized size = 1.04 \[ \frac {\left (d \,x^{3}+c \,x^{2}+b x +a \right )^{p +1}}{x^{2}} \]
Verification of antiderivative is not currently implemented for this CAS.
[In]
[Out]
________________________________________________________________________________________
maxima [A] time = 0.64, size = 36, normalized size = 1.57 \[ \frac {{\left (d x^{3} + c x^{2} + b x + a\right )} {\left (d x^{3} + c x^{2} + b x + a\right )}^{p}}{x^{2}} \]
Verification of antiderivative is not currently implemented for this CAS.
[In]
[Out]
________________________________________________________________________________________
mupad [B] time = 3.32, size = 23, normalized size = 1.00 \[ \frac {{\left (d\,x^3+c\,x^2+b\,x+a\right )}^{p+1}}{x^2} \]
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]
________________________________________________________________________________________