Optimal. Leaf size=20 \[ \frac{x^{p+1} (b+c x)^{p+1}}{p+1} \]
[Out]
________________________________________________________________________________________
Rubi [A] time = 0.003549, antiderivative size = 20, normalized size of antiderivative = 1., number of steps used = 1, number of rules used = 1, integrand size = 17, \(\frac{\text{number of rules}}{\text{integrand size}}\) = 0.059, Rules used = {74} \[ \frac{x^{p+1} (b+c x)^{p+1}}{p+1} \]
Antiderivative was successfully verified.
[In]
[Out]
Rule 74
Rubi steps
\begin{align*} \int x^p (b+c x)^p (b+2 c x) \, dx &=\frac{x^{1+p} (b+c x)^{1+p}}{1+p}\\ \end{align*}
Mathematica [A] time = 0.0109254, size = 20, normalized size = 1. \[ \frac{x^{p+1} (b+c x)^{p+1}}{p+1} \]
Antiderivative was successfully verified.
[In]
[Out]
________________________________________________________________________________________
Maple [A] time = 0.003, size = 21, normalized size = 1.1 \begin{align*}{\frac{{x}^{1+p} \left ( cx+b \right ) ^{1+p}}{1+p}} \end{align*}
Verification of antiderivative is not currently implemented for this CAS.
[In]
[Out]
________________________________________________________________________________________
Maxima [A] time = 1.08433, size = 39, normalized size = 1.95 \begin{align*} \frac{{\left (c x^{2} + b x\right )} e^{\left (p \log \left (c x + b\right ) + p \log \left (x\right )\right )}}{p + 1} \end{align*}
Verification of antiderivative is not currently implemented for this CAS.
[In]
[Out]
________________________________________________________________________________________
Fricas [A] time = 1.01109, size = 53, normalized size = 2.65 \begin{align*} \frac{{\left (c x^{2} + b x\right )}{\left (c x + b\right )}^{p} x^{p}}{p + 1} \end{align*}
Verification of antiderivative is not currently implemented for this CAS.
[In]
[Out]
________________________________________________________________________________________
Sympy [A] time = 2.89365, size = 46, normalized size = 2.3 \begin{align*} \begin{cases} \frac{b x x^{p} \left (b + c x\right )^{p}}{p + 1} + \frac{c x^{2} x^{p} \left (b + c x\right )^{p}}{p + 1} & \text{for}\: p \neq -1 \\\log{\left (x \right )} + \log{\left (\frac{b}{c} + x \right )} & \text{otherwise} \end{cases} \end{align*}
Verification of antiderivative is not currently implemented for this CAS.
[In]
[Out]
________________________________________________________________________________________
Giac [A] time = 1.57675, size = 47, normalized size = 2.35 \begin{align*} \frac{{\left (c x + b\right )}^{p} c x^{2} x^{p} +{\left (c x + b\right )}^{p} b x x^{p}}{p + 1} \end{align*}
Verification of antiderivative is not currently implemented for this CAS.
[In]
[Out]