Optimal. Leaf size=30 \[ \frac{\left (a+b (c+d x)^4\right )^{p+1}}{4 b d (p+1)} \]
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Rubi [A] time = 0.0272146, antiderivative size = 30, normalized size of antiderivative = 1., number of steps used = 1, number of rules used = 1, integrand size = 21, \(\frac{\text{number of rules}}{\text{integrand size}}\) = 0.048 \[ \frac{\left (a+b (c+d x)^4\right )^{p+1}}{4 b d (p+1)} \]
Antiderivative was successfully verified.
[In] Int[(c + d*x)^3*(a + b*(c + d*x)^4)^p,x]
[Out]
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Rubi in Sympy [A] time = 4.9432, size = 20, normalized size = 0.67 \[ \frac{\left (a + b \left (c + d x\right )^{4}\right )^{p + 1}}{4 b d \left (p + 1\right )} \]
Verification of antiderivative is not currently implemented for this CAS.
[In] rubi_integrate((d*x+c)**3*(a+b*(d*x+c)**4)**p,x)
[Out]
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Mathematica [A] time = 0.0328594, size = 32, normalized size = 1.07 \[ \frac{\left (a+b (c+d x)^4\right )^{p+1}}{2 d (2 b p+2 b)} \]
Antiderivative was successfully verified.
[In] Integrate[(c + d*x)^3*(a + b*(c + d*x)^4)^p,x]
[Out]
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Maple [B] time = 0.01, size = 63, normalized size = 2.1 \[{\frac{ \left ( b{d}^{4}{x}^{4}+4\,bc{d}^{3}{x}^{3}+6\,b{c}^{2}{d}^{2}{x}^{2}+4\,b{c}^{3}dx+b{c}^{4}+a \right ) ^{1+p}}{4\,bd \left ( 1+p \right ) }} \]
Verification of antiderivative is not currently implemented for this CAS.
[In] int((d*x+c)^3*(a+b*(d*x+c)^4)^p,x)
[Out]
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Maxima [F] time = 0., size = 0, normalized size = 0. \[ \text{Exception raised: ValueError} \]
Verification of antiderivative is not currently implemented for this CAS.
[In] integrate((d*x + c)^3*((d*x + c)^4*b + a)^p,x, algorithm="maxima")
[Out]
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Fricas [A] time = 0.224008, size = 140, normalized size = 4.67 \[ \frac{{\left (b d^{4} x^{4} + 4 \, b c d^{3} x^{3} + 6 \, b c^{2} d^{2} x^{2} + 4 \, b c^{3} d x + b c^{4} + a\right )}{\left (b d^{4} x^{4} + 4 \, b c d^{3} x^{3} + 6 \, b c^{2} d^{2} x^{2} + 4 \, b c^{3} d x + b c^{4} + a\right )}^{p}}{4 \,{\left (b d p + b d\right )}} \]
Verification of antiderivative is not currently implemented for this CAS.
[In] integrate((d*x + c)^3*((d*x + c)^4*b + a)^p,x, algorithm="fricas")
[Out]
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Sympy [F(-1)] time = 0., size = 0, normalized size = 0. \[ \text{Timed out} \]
Verification of antiderivative is not currently implemented for this CAS.
[In] integrate((d*x+c)**3*(a+b*(d*x+c)**4)**p,x)
[Out]
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GIAC/XCAS [A] time = 0.217122, size = 38, normalized size = 1.27 \[ \frac{{\left ({\left (d x + c\right )}^{4} b + a\right )}^{p + 1}}{4 \, b d{\left (p + 1\right )}} \]
Verification of antiderivative is not currently implemented for this CAS.
[In] integrate((d*x + c)^3*((d*x + c)^4*b + a)^p,x, algorithm="giac")
[Out]