Optimal. Leaf size=157 \[ -\frac{b (2 a d+b c)}{(a+b x) (b c-a d)^4}+\frac{a b}{2 (a+b x)^2 (b c-a d)^3}-\frac{d (a d+2 b c)}{(c+d x) (b c-a d)^4}-\frac{c d}{2 (c+d x)^2 (b c-a d)^3}-\frac{3 b d (a d+b c) \log (a+b x)}{(b c-a d)^5}+\frac{3 b d (a d+b c) \log (c+d x)}{(b c-a d)^5} \]
[Out]
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Rubi [A] time = 0.311724, antiderivative size = 157, normalized size of antiderivative = 1., number of steps used = 2, number of rules used = 1, integrand size = 16, \(\frac{\text{number of rules}}{\text{integrand size}}\) = 0.062 \[ -\frac{b (2 a d+b c)}{(a+b x) (b c-a d)^4}+\frac{a b}{2 (a+b x)^2 (b c-a d)^3}-\frac{d (a d+2 b c)}{(c+d x) (b c-a d)^4}-\frac{c d}{2 (c+d x)^2 (b c-a d)^3}-\frac{3 b d (a d+b c) \log (a+b x)}{(b c-a d)^5}+\frac{3 b d (a d+b c) \log (c+d x)}{(b c-a d)^5} \]
Antiderivative was successfully verified.
[In] Int[x/((a + b*x)^3*(c + d*x)^3),x]
[Out]
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Rubi in Sympy [A] time = 77.5712, size = 141, normalized size = 0.9 \[ - \frac{a b}{2 \left (a + b x\right )^{2} \left (a d - b c\right )^{3}} + \frac{3 b d \left (a d + b c\right ) \log{\left (a + b x \right )}}{\left (a d - b c\right )^{5}} - \frac{3 b d \left (a d + b c\right ) \log{\left (c + d x \right )}}{\left (a d - b c\right )^{5}} - \frac{b \left (2 a d + b c\right )}{\left (a + b x\right ) \left (a d - b c\right )^{4}} + \frac{c d}{2 \left (c + d x\right )^{2} \left (a d - b c\right )^{3}} - \frac{d \left (a d + 2 b c\right )}{\left (c + d x\right ) \left (a d - b c\right )^{4}} \]
Verification of antiderivative is not currently implemented for this CAS.
[In] rubi_integrate(x/(b*x+a)**3/(d*x+c)**3,x)
[Out]
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Mathematica [A] time = 0.260098, size = 142, normalized size = 0.9 \[ \frac{\frac{a b (b c-a d)^2}{(a+b x)^2}-\frac{c d (b c-a d)^2}{(c+d x)^2}-\frac{2 b (2 a d+b c) (b c-a d)}{a+b x}+\frac{2 d (a d-b c) (a d+2 b c)}{c+d x}-6 b d (a d+b c) \log (a+b x)+6 b d (a d+b c) \log (c+d x)}{2 (b c-a d)^5} \]
Antiderivative was successfully verified.
[In] Integrate[x/((a + b*x)^3*(c + d*x)^3),x]
[Out]
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Maple [A] time = 0.02, size = 226, normalized size = 1.4 \[ -{\frac{{d}^{2}a}{ \left ( ad-bc \right ) ^{4} \left ( dx+c \right ) }}-2\,{\frac{bdc}{ \left ( ad-bc \right ) ^{4} \left ( dx+c \right ) }}+{\frac{cd}{2\, \left ( ad-bc \right ) ^{3} \left ( dx+c \right ) ^{2}}}-3\,{\frac{{d}^{2}b\ln \left ( dx+c \right ) a}{ \left ( ad-bc \right ) ^{5}}}-3\,{\frac{{b}^{2}d\ln \left ( dx+c \right ) c}{ \left ( ad-bc \right ) ^{5}}}-{\frac{ab}{2\, \left ( ad-bc \right ) ^{3} \left ( bx+a \right ) ^{2}}}-2\,{\frac{abd}{ \left ( ad-bc \right ) ^{4} \left ( bx+a \right ) }}-{\frac{{b}^{2}c}{ \left ( ad-bc \right ) ^{4} \left ( bx+a \right ) }}+3\,{\frac{{d}^{2}b\ln \left ( bx+a \right ) a}{ \left ( ad-bc \right ) ^{5}}}+3\,{\frac{{b}^{2}d\ln \left ( bx+a \right ) c}{ \left ( ad-bc \right ) ^{5}}} \]
Verification of antiderivative is not currently implemented for this CAS.
[In] int(x/(b*x+a)^3/(d*x+c)^3,x)
[Out]
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Maxima [A] time = 1.38963, size = 846, normalized size = 5.39 \[ -\frac{3 \,{\left (b^{2} c d + a b d^{2}\right )} \log \left (b x + a\right )}{b^{5} c^{5} - 5 \, a b^{4} c^{4} d + 10 \, a^{2} b^{3} c^{3} d^{2} - 10 \, a^{3} b^{2} c^{2} d^{3} + 5 \, a^{4} b c d^{4} - a^{5} d^{5}} + \frac{3 \,{\left (b^{2} c d + a b d^{2}\right )} \log \left (d x + c\right )}{b^{5} c^{5} - 5 \, a b^{4} c^{4} d + 10 \, a^{2} b^{3} c^{3} d^{2} - 10 \, a^{3} b^{2} c^{2} d^{3} + 5 \, a^{4} b c d^{4} - a^{5} d^{5}} - \frac{a b^{2} c^{3} + 10 \, a^{2} b c^{2} d + a^{3} c d^{2} + 6 \,{\left (b^{3} c d^{2} + a b^{2} d^{3}\right )} x^{3} + 9 \,{\left (b^{3} c^{2} d + 2 \, a b^{2} c d^{2} + a^{2} b d^{3}\right )} x^{2} + 2 \,{\left (b^{3} c^{3} + 8 \, a b^{2} c^{2} d + 8 \, a^{2} b c d^{2} + a^{3} d^{3}\right )} x}{2 \,{\left (a^{2} b^{4} c^{6} - 4 \, a^{3} b^{3} c^{5} d + 6 \, a^{4} b^{2} c^{4} d^{2} - 4 \, a^{5} b c^{3} d^{3} + a^{6} c^{2} d^{4} +{\left (b^{6} c^{4} d^{2} - 4 \, a b^{5} c^{3} d^{3} + 6 \, a^{2} b^{4} c^{2} d^{4} - 4 \, a^{3} b^{3} c d^{5} + a^{4} b^{2} d^{6}\right )} x^{4} + 2 \,{\left (b^{6} c^{5} d - 3 \, a b^{5} c^{4} d^{2} + 2 \, a^{2} b^{4} c^{3} d^{3} + 2 \, a^{3} b^{3} c^{2} d^{4} - 3 \, a^{4} b^{2} c d^{5} + a^{5} b d^{6}\right )} x^{3} +{\left (b^{6} c^{6} - 9 \, a^{2} b^{4} c^{4} d^{2} + 16 \, a^{3} b^{3} c^{3} d^{3} - 9 \, a^{4} b^{2} c^{2} d^{4} + a^{6} d^{6}\right )} x^{2} + 2 \,{\left (a b^{5} c^{6} - 3 \, a^{2} b^{4} c^{5} d + 2 \, a^{3} b^{3} c^{4} d^{2} + 2 \, a^{4} b^{2} c^{3} d^{3} - 3 \, a^{5} b c^{2} d^{4} + a^{6} c d^{5}\right )} x\right )}} \]
Verification of antiderivative is not currently implemented for this CAS.
[In] integrate(x/((b*x + a)^3*(d*x + c)^3),x, algorithm="maxima")
[Out]
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Fricas [A] time = 0.230147, size = 1203, normalized size = 7.66 \[ \text{result too large to display} \]
Verification of antiderivative is not currently implemented for this CAS.
[In] integrate(x/((b*x + a)^3*(d*x + c)^3),x, algorithm="fricas")
[Out]
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Sympy [A] time = 18.5963, size = 1047, normalized size = 6.67 \[ \text{result too large to display} \]
Verification of antiderivative is not currently implemented for this CAS.
[In] integrate(x/(b*x+a)**3/(d*x+c)**3,x)
[Out]
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GIAC/XCAS [F(-2)] time = 0., size = 0, normalized size = 0. \[ \text{Exception raised: NotImplementedError} \]
Verification of antiderivative is not currently implemented for this CAS.
[In] integrate(x/((b*x + a)^3*(d*x + c)^3),x, algorithm="giac")
[Out]