Optimal. Leaf size=255 \[ \frac{32 b^3 (a+b x)^{7/2} (-15 a B e+8 A b e+7 b B d)}{45045 e (d+e x)^{7/2} (b d-a e)^5}+\frac{16 b^2 (a+b x)^{7/2} (-15 a B e+8 A b e+7 b B d)}{6435 e (d+e x)^{9/2} (b d-a e)^4}+\frac{4 b (a+b x)^{7/2} (-15 a B e+8 A b e+7 b B d)}{715 e (d+e x)^{11/2} (b d-a e)^3}+\frac{2 (a+b x)^{7/2} (-15 a B e+8 A b e+7 b B d)}{195 e (d+e x)^{13/2} (b d-a e)^2}-\frac{2 (a+b x)^{7/2} (B d-A e)}{15 e (d+e x)^{15/2} (b d-a e)} \]
[Out]
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Rubi [A] time = 0.469568, antiderivative size = 255, normalized size of antiderivative = 1., number of steps used = 5, number of rules used = 3, integrand size = 24, \(\frac{\text{number of rules}}{\text{integrand size}}\) = 0.125 \[ \frac{32 b^3 (a+b x)^{7/2} (-15 a B e+8 A b e+7 b B d)}{45045 e (d+e x)^{7/2} (b d-a e)^5}+\frac{16 b^2 (a+b x)^{7/2} (-15 a B e+8 A b e+7 b B d)}{6435 e (d+e x)^{9/2} (b d-a e)^4}+\frac{4 b (a+b x)^{7/2} (-15 a B e+8 A b e+7 b B d)}{715 e (d+e x)^{11/2} (b d-a e)^3}+\frac{2 (a+b x)^{7/2} (-15 a B e+8 A b e+7 b B d)}{195 e (d+e x)^{13/2} (b d-a e)^2}-\frac{2 (a+b x)^{7/2} (B d-A e)}{15 e (d+e x)^{15/2} (b d-a e)} \]
Antiderivative was successfully verified.
[In] Int[((a + b*x)^(5/2)*(A + B*x))/(d + e*x)^(17/2),x]
[Out]
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Rubi in Sympy [A] time = 50.7058, size = 246, normalized size = 0.96 \[ - \frac{32 b^{3} \left (a + b x\right )^{\frac{7}{2}} \left (8 A b e - 15 B a e + 7 B b d\right )}{45045 e \left (d + e x\right )^{\frac{7}{2}} \left (a e - b d\right )^{5}} + \frac{16 b^{2} \left (a + b x\right )^{\frac{7}{2}} \left (8 A b e - 15 B a e + 7 B b d\right )}{6435 e \left (d + e x\right )^{\frac{9}{2}} \left (a e - b d\right )^{4}} - \frac{4 b \left (a + b x\right )^{\frac{7}{2}} \left (8 A b e - 15 B a e + 7 B b d\right )}{715 e \left (d + e x\right )^{\frac{11}{2}} \left (a e - b d\right )^{3}} + \frac{2 \left (a + b x\right )^{\frac{7}{2}} \left (8 A b e - 15 B a e + 7 B b d\right )}{195 e \left (d + e x\right )^{\frac{13}{2}} \left (a e - b d\right )^{2}} - \frac{2 \left (a + b x\right )^{\frac{7}{2}} \left (A e - B d\right )}{15 e \left (d + e x\right )^{\frac{15}{2}} \left (a e - b d\right )} \]
Verification of antiderivative is not currently implemented for this CAS.
[In] rubi_integrate((b*x+a)**(5/2)*(B*x+A)/(e*x+d)**(17/2),x)
[Out]
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Mathematica [A] time = 0.732623, size = 292, normalized size = 1.15 \[ \frac{2 \sqrt{a+b x} \left (\frac{16 b^6 (d+e x)^7 (-15 a B e+8 A b e+7 b B d)}{(b d-a e)^5}+\frac{8 b^5 (d+e x)^6 (-15 a B e+8 A b e+7 b B d)}{(b d-a e)^4}+\frac{6 b^4 (d+e x)^5 (-15 a B e+8 A b e+7 b B d)}{(b d-a e)^3}+\frac{5 b^3 (d+e x)^4 (-15 a B e+8 A b e+7 b B d)}{(b d-a e)^2}-\frac{35 b^2 (d+e x)^3 (159 a B e+A b e-160 b B d)}{a e-b d}+63 b (d+e x)^2 (-135 a B e-71 A b e+206 b B d)-231 (d+e x) (a e-b d) (15 a B e+31 A b e-46 b B d)+3003 (b d-a e)^2 (B d-A e)\right )}{45045 e^4 (d+e x)^{15/2}} \]
Antiderivative was successfully verified.
[In] Integrate[((a + b*x)^(5/2)*(A + B*x))/(d + e*x)^(17/2),x]
[Out]
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Maple [B] time = 0.015, size = 505, normalized size = 2. \[ -{\frac{256\,A{b}^{4}{e}^{4}{x}^{4}-480\,Ba{b}^{3}{e}^{4}{x}^{4}+224\,B{b}^{4}d{e}^{3}{x}^{4}-896\,Aa{b}^{3}{e}^{4}{x}^{3}+1920\,A{b}^{4}d{e}^{3}{x}^{3}+1680\,B{a}^{2}{b}^{2}{e}^{4}{x}^{3}-4384\,Ba{b}^{3}d{e}^{3}{x}^{3}+1680\,B{b}^{4}{d}^{2}{e}^{2}{x}^{3}+2016\,A{a}^{2}{b}^{2}{e}^{4}{x}^{2}-6720\,Aa{b}^{3}d{e}^{3}{x}^{2}+6240\,A{b}^{4}{d}^{2}{e}^{2}{x}^{2}-3780\,B{a}^{3}b{e}^{4}{x}^{2}+14364\,B{a}^{2}{b}^{2}d{e}^{3}{x}^{2}-17580\,Ba{b}^{3}{d}^{2}{e}^{2}{x}^{2}+5460\,B{b}^{4}{d}^{3}e{x}^{2}-3696\,A{a}^{3}b{e}^{4}x+15120\,A{a}^{2}{b}^{2}d{e}^{3}x-21840\,Aa{b}^{3}{d}^{2}{e}^{2}x+11440\,A{b}^{4}{d}^{3}ex+6930\,B{a}^{4}{e}^{4}x-31584\,B{a}^{3}bd{e}^{3}x+54180\,B{a}^{2}{b}^{2}{d}^{2}{e}^{2}x-40560\,Ba{b}^{3}{d}^{3}ex+10010\,B{b}^{4}{d}^{4}x+6006\,A{a}^{4}{e}^{4}-27720\,A{a}^{3}bd{e}^{3}+49140\,A{a}^{2}{b}^{2}{d}^{2}{e}^{2}-40040\,Aa{b}^{3}{d}^{3}e+12870\,A{b}^{4}{d}^{4}+924\,B{a}^{4}d{e}^{3}-3780\,B{a}^{3}b{d}^{2}{e}^{2}+5460\,B{a}^{2}{b}^{2}{d}^{3}e-2860\,Ba{b}^{3}{d}^{4}}{45045\,{a}^{5}{e}^{5}-225225\,{a}^{4}bd{e}^{4}+450450\,{a}^{3}{b}^{2}{d}^{2}{e}^{3}-450450\,{a}^{2}{b}^{3}{d}^{3}{e}^{2}+225225\,a{b}^{4}{d}^{4}e-45045\,{b}^{5}{d}^{5}} \left ( bx+a \right ) ^{{\frac{7}{2}}} \left ( ex+d \right ) ^{-{\frac{15}{2}}}} \]
Verification of antiderivative is not currently implemented for this CAS.
[In] int((b*x+a)^(5/2)*(B*x+A)/(e*x+d)^(17/2),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((B*x + A)*(b*x + a)^(5/2)/(e*x + d)^(17/2),x, algorithm="maxima")
[Out]
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Fricas [A] time = 32.7565, size = 1978, normalized size = 7.76 \[ \text{result too large to display} \]
Verification of antiderivative is not currently implemented for this CAS.
[In] integrate((B*x + A)*(b*x + a)^(5/2)/(e*x + d)^(17/2),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((b*x+a)**(5/2)*(B*x+A)/(e*x+d)**(17/2),x)
[Out]
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GIAC/XCAS [A] time = 0.750125, size = 1, normalized size = 0. \[ \mathit{Done} \]
Verification of antiderivative is not currently implemented for this CAS.
[In] integrate((B*x + A)*(b*x + a)^(5/2)/(e*x + d)^(17/2),x, algorithm="giac")
[Out]