Optimal. Leaf size=55 \[ -\frac{\left (-\frac{c x}{b}\right )^{-p-1} \left (b x+c x^2\right )^{p+1} \, _2F_1\left (-p,p+1;p+2;\frac{b+c x}{b}\right )}{b (p+1)} \]
[Out]
_______________________________________________________________________________________
Rubi [A] time = 0.0321692, antiderivative size = 55, normalized size of antiderivative = 1., number of steps used = 1, number of rules used = 1, integrand size = 11, \(\frac{\text{number of rules}}{\text{integrand size}}\) = 0.091 \[ -\frac{\left (-\frac{c x}{b}\right )^{-p-1} \left (b x+c x^2\right )^{p+1} \, _2F_1\left (-p,p+1;p+2;\frac{b+c x}{b}\right )}{b (p+1)} \]
Antiderivative was successfully verified.
[In] Int[(b*x + c*x^2)^p,x]
[Out]
_______________________________________________________________________________________
Rubi in Sympy [A] time = 2.75342, size = 42, normalized size = 0.76 \[ - \frac{\left (- \frac{c x}{b}\right )^{- p - 1} \left (b x + c x^{2}\right )^{p + 1}{{}_{2}F_{1}\left (\begin{matrix} - p, p + 1 \\ p + 2 \end{matrix}\middle |{\frac{b + c x}{b}} \right )}}{b \left (p + 1\right )} \]
Verification of antiderivative is not currently implemented for this CAS.
[In] rubi_integrate((c*x**2+b*x)**p,x)
[Out]
_______________________________________________________________________________________
Mathematica [A] time = 0.0407748, size = 45, normalized size = 0.82 \[ \frac{x (x (b+c x))^p \left (\frac{c x}{b}+1\right )^{-p} \, _2F_1\left (-p,p+1;p+2;-\frac{c x}{b}\right )}{p+1} \]
Antiderivative was successfully verified.
[In] Integrate[(b*x + c*x^2)^p,x]
[Out]
_______________________________________________________________________________________
Maple [F] time = 0.044, size = 0, normalized size = 0. \[ \int \left ( c{x}^{2}+bx \right ) ^{p}\, dx \]
Verification of antiderivative is not currently implemented for this CAS.
[In] int((c*x^2+b*x)^p,x)
[Out]
_______________________________________________________________________________________
Maxima [F] time = 0., size = 0, normalized size = 0. \[ \int{\left (c x^{2} + b x\right )}^{p}\,{d x} \]
Verification of antiderivative is not currently implemented for this CAS.
[In] integrate((c*x^2 + b*x)^p,x, algorithm="maxima")
[Out]
_______________________________________________________________________________________
Fricas [F] time = 0., size = 0, normalized size = 0. \[{\rm integral}\left ({\left (c x^{2} + b x\right )}^{p}, x\right ) \]
Verification of antiderivative is not currently implemented for this CAS.
[In] integrate((c*x^2 + b*x)^p,x, algorithm="fricas")
[Out]
_______________________________________________________________________________________
Sympy [F] time = 0., size = 0, normalized size = 0. \[ \int \left (b x + c x^{2}\right )^{p}\, dx \]
Verification of antiderivative is not currently implemented for this CAS.
[In] integrate((c*x**2+b*x)**p,x)
[Out]
_______________________________________________________________________________________
GIAC/XCAS [F] time = 0., size = 0, normalized size = 0. \[ \int{\left (c x^{2} + b x\right )}^{p}\,{d x} \]
Verification of antiderivative is not currently implemented for this CAS.
[In] integrate((c*x^2 + b*x)^p,x, algorithm="giac")
[Out]