Optimal. Leaf size=51 \[ -\frac{(c+d x)^{n+1} \, _2F_1\left (1,n+1;n+2;\frac{b (c+d x)}{b c-a d}\right )}{(n+1) (b c-a d)} \]
[Out]
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Rubi [A] time = 0.0352512, antiderivative size = 51, normalized size of antiderivative = 1., number of steps used = 1, number of rules used = 1, integrand size = 15, \(\frac{\text{number of rules}}{\text{integrand size}}\) = 0.067 \[ -\frac{(c+d x)^{n+1} \, _2F_1\left (1,n+1;n+2;\frac{b (c+d x)}{b c-a d}\right )}{(n+1) (b c-a d)} \]
Antiderivative was successfully verified.
[In] Int[(c + d*x)^n/(a + b*x),x]
[Out]
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Rubi in Sympy [A] time = 5.43047, size = 37, normalized size = 0.73 \[ \frac{\left (c + d x\right )^{n + 1}{{}_{2}F_{1}\left (\begin{matrix} 1, n + 1 \\ n + 2 \end{matrix}\middle |{\frac{b \left (- c - d x\right )}{a d - b c}} \right )}}{\left (n + 1\right ) \left (a d - b c\right )} \]
Verification of antiderivative is not currently implemented for this CAS.
[In] rubi_integrate((d*x+c)**n/(b*x+a),x)
[Out]
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Mathematica [A] time = 0.0334955, size = 51, normalized size = 1. \[ -\frac{(c+d x)^{n+1} \, _2F_1\left (1,n+1;n+2;\frac{b (c+d x)}{b c-a d}\right )}{(n+1) (b c-a d)} \]
Antiderivative was successfully verified.
[In] Integrate[(c + d*x)^n/(a + b*x),x]
[Out]
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Maple [F] time = 0.061, size = 0, normalized size = 0. \[ \int{\frac{ \left ( dx+c \right ) ^{n}}{bx+a}}\, dx \]
Verification of antiderivative is not currently implemented for this CAS.
[In] int((d*x+c)^n/(b*x+a),x)
[Out]
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Maxima [F] time = 0., size = 0, normalized size = 0. \[ \int \frac{{\left (d x + c\right )}^{n}}{b x + a}\,{d x} \]
Verification of antiderivative is not currently implemented for this CAS.
[In] integrate((d*x + c)^n/(b*x + a),x, algorithm="maxima")
[Out]
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Fricas [F] time = 0., size = 0, normalized size = 0. \[{\rm integral}\left (\frac{{\left (d x + c\right )}^{n}}{b x + a}, x\right ) \]
Verification of antiderivative is not currently implemented for this CAS.
[In] integrate((d*x + c)^n/(b*x + a),x, algorithm="fricas")
[Out]
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Sympy [F] time = 0., size = 0, normalized size = 0. \[ \int \frac{\left (c + d x\right )^{n}}{a + b x}\, dx \]
Verification of antiderivative is not currently implemented for this CAS.
[In] integrate((d*x+c)**n/(b*x+a),x)
[Out]
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GIAC/XCAS [F] time = 0., size = 0, normalized size = 0. \[ \int \frac{{\left (d x + c\right )}^{n}}{b x + a}\,{d x} \]
Verification of antiderivative is not currently implemented for this CAS.
[In] integrate((d*x + c)^n/(b*x + a),x, algorithm="giac")
[Out]