3.27.98 \(\int \frac {\sqrt {1-2 x}}{(2+3 x)^{7/2} (3+5 x)^{5/2}} \, dx\) [2698]

Optimal. Leaf size=218 \[ \frac {2 \sqrt {1-2 x}}{5 (2+3 x)^{5/2} (3+5 x)^{3/2}}+\frac {556 \sqrt {1-2 x}}{105 (2+3 x)^{3/2} (3+5 x)^{3/2}}+\frac {116044 \sqrt {1-2 x}}{735 \sqrt {2+3 x} (3+5 x)^{3/2}}-\frac {155104 \sqrt {1-2 x} \sqrt {2+3 x}}{147 (3+5 x)^{3/2}}+\frac {10312712 \sqrt {1-2 x} \sqrt {2+3 x}}{1617 \sqrt {3+5 x}}-\frac {10312712 E\left (\sin ^{-1}\left (\sqrt {\frac {3}{7}} \sqrt {1-2 x}\right )|\frac {35}{33}\right )}{245 \sqrt {33}}-\frac {310208 F\left (\sin ^{-1}\left (\sqrt {\frac {3}{7}} \sqrt {1-2 x}\right )|\frac {35}{33}\right )}{245 \sqrt {33}} \]

[Out]

-10312712/8085*EllipticE(1/7*21^(1/2)*(1-2*x)^(1/2),1/33*1155^(1/2))*33^(1/2)-310208/8085*EllipticF(1/7*21^(1/
2)*(1-2*x)^(1/2),1/33*1155^(1/2))*33^(1/2)+2/5*(1-2*x)^(1/2)/(2+3*x)^(5/2)/(3+5*x)^(3/2)+556/105*(1-2*x)^(1/2)
/(2+3*x)^(3/2)/(3+5*x)^(3/2)+116044/735*(1-2*x)^(1/2)/(3+5*x)^(3/2)/(2+3*x)^(1/2)-155104/147*(1-2*x)^(1/2)*(2+
3*x)^(1/2)/(3+5*x)^(3/2)[phone]/1617*(1-2*x)^(1/2)*(2+3*x)^(1/2)/(3+5*x)^(1/2)

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Rubi [A]
time = 0.06, antiderivative size = 218, normalized size of antiderivative = 1.00, number of steps used = 8, number of rules used = 5, integrand size = 28, \(\frac {\text {number of rules}}{\text {integrand size}}\) = 0.179, Rules used = {101, 157, 164, 114, 120} \begin {gather*} -\frac {310208 F\left (\text {ArcSin}\left (\sqrt {\frac {3}{7}} \sqrt {1-2 x}\right )|\frac {35}{33}\right )}{245 \sqrt {33}}-\frac {10312712 E\left (\text {ArcSin}\left (\sqrt {\frac {3}{7}} \sqrt {1-2 x}\right )|\frac {35}{33}\right )}{245 \sqrt {33}}+\frac {10312712 \sqrt {1-2 x} \sqrt {3 x+2}}{1617 \sqrt {5 x+3}}-\frac {155104 \sqrt {1-2 x} \sqrt {3 x+2}}{147 (5 x+3)^{3/2}}+\frac {116044 \sqrt {1-2 x}}{735 \sqrt {3 x+2} (5 x+3)^{3/2}}+\frac {556 \sqrt {1-2 x}}{105 (3 x+2)^{3/2} (5 x+3)^{3/2}}+\frac {2 \sqrt {1-2 x}}{5 (3 x+2)^{5/2} (5 x+3)^{3/2}} \end {gather*}

Antiderivative was successfully verified.

[In]

Int[Sqrt[1 - 2*x]/((2 + 3*x)^(7/2)*(3 + 5*x)^(5/2)),x]

[Out]

(2*Sqrt[1 - 2*x])/(5*(2 + 3*x)^(5/2)*(3 + 5*x)^(3/2)) + (556*Sqrt[1 - 2*x])/(105*(2 + 3*x)^(3/2)*(3 + 5*x)^(3/
2)) + (116044*Sqrt[1 - 2*x])/(735*Sqrt[2 + 3*x]*(3 + 5*x)^(3/2)) - (155104*Sqrt[1 - 2*x]*Sqrt[2 + 3*x])/(147*(
3 + 5*x)^(3/2)) + (10312712*Sqrt[1 - 2*x]*Sqrt[2 + 3*x])/(1617*Sqrt[3 + 5*x]) - (10312712*EllipticE[ArcSin[Sqr
t[3/7]*Sqrt[1 - 2*x]], 35/33])/(245*Sqrt[33]) - (310208*EllipticF[ArcSin[Sqrt[3/7]*Sqrt[1 - 2*x]], 35/33])/(24
5*Sqrt[33])

Rule 101

Int[((a_.) + (b_.)*(x_))^(m_)*((c_.) + (d_.)*(x_))^(n_.)*((e_.) + (f_.)*(x_))^(p_.), x_Symbol] :> Simp[(a + b*
x)^(m + 1)*(c + d*x)^n*((e + f*x)^(p + 1)/((m + 1)*(b*e - a*f))), x] - Dist[1/((m + 1)*(b*e - a*f)), Int[(a +
b*x)^(m + 1)*(c + d*x)^(n - 1)*(e + f*x)^p*Simp[d*e*n + c*f*(m + p + 2) + d*f*(m + n + p + 2)*x, x], x], x] /;
FreeQ[{a, b, c, d, e, f, p}, x] && LtQ[m, -1] && GtQ[n, 0] && (IntegersQ[2*m, 2*n, 2*p] || IntegersQ[m, n + p
] || IntegersQ[p, m + n])

Rule 114

Int[Sqrt[(e_.) + (f_.)*(x_)]/(Sqrt[(a_) + (b_.)*(x_)]*Sqrt[(c_) + (d_.)*(x_)]), x_Symbol] :> Simp[(2/b)*Rt[-(b
*e - a*f)/d, 2]*EllipticE[ArcSin[Sqrt[a + b*x]/Rt[-(b*c - a*d)/d, 2]], f*((b*c - a*d)/(d*(b*e - a*f)))], x] /;
FreeQ[{a, b, c, d, e, f}, x] && GtQ[b/(b*c - a*d), 0] && GtQ[b/(b*e - a*f), 0] &&  !LtQ[-(b*c - a*d)/d, 0] &&
!(SimplerQ[c + d*x, a + b*x] && GtQ[-d/(b*c - a*d), 0] && GtQ[d/(d*e - c*f), 0] &&  !LtQ[(b*c - a*d)/b, 0])

Rule 120

Int[1/(Sqrt[(a_) + (b_.)*(x_)]*Sqrt[(c_) + (d_.)*(x_)]*Sqrt[(e_) + (f_.)*(x_)]), x_Symbol] :> Simp[2*(Rt[-b/d,
2]/(b*Sqrt[(b*e - a*f)/b]))*EllipticF[ArcSin[Sqrt[a + b*x]/(Rt[-b/d, 2]*Sqrt[(b*c - a*d)/b])], f*((b*c - a*d)
/(d*(b*e - a*f)))], x] /; FreeQ[{a, b, c, d, e, f}, x] && GtQ[(b*c - a*d)/b, 0] && GtQ[(b*e - a*f)/b, 0] && Po
sQ[-b/d] &&  !(SimplerQ[c + d*x, a + b*x] && GtQ[(d*e - c*f)/d, 0] && GtQ[-d/b, 0]) &&  !(SimplerQ[c + d*x, a
+ b*x] && GtQ[((-b)*e + a*f)/f, 0] && GtQ[-f/b, 0]) &&  !(SimplerQ[e + f*x, a + b*x] && GtQ[((-d)*e + c*f)/f,
0] && GtQ[((-b)*e + a*f)/f, 0] && (PosQ[-f/d] || PosQ[-f/b]))

Rule 157

Int[((a_.) + (b_.)*(x_))^(m_)*((c_.) + (d_.)*(x_))^(n_)*((e_.) + (f_.)*(x_))^(p_)*((g_.) + (h_.)*(x_)), x_Symb
ol] :> Simp[(b*g - a*h)*(a + b*x)^(m + 1)*(c + d*x)^(n + 1)*((e + f*x)^(p + 1)/((m + 1)*(b*c - a*d)*(b*e - a*f
))), x] + Dist[1/((m + 1)*(b*c - a*d)*(b*e - a*f)), Int[(a + b*x)^(m + 1)*(c + d*x)^n*(e + f*x)^p*Simp[(a*d*f*
g - b*(d*e + c*f)*g + b*c*e*h)*(m + 1) - (b*g - a*h)*(d*e*(n + 1) + c*f*(p + 1)) - d*f*(b*g - a*h)*(m + n + p
+ 3)*x, x], x], x] /; FreeQ[{a, b, c, d, e, f, g, h, n, p}, x] && LtQ[m, -1] && IntegersQ[2*m, 2*n, 2*p]

Rule 164

Int[((g_.) + (h_.)*(x_))/(Sqrt[(a_.) + (b_.)*(x_)]*Sqrt[(c_) + (d_.)*(x_)]*Sqrt[(e_) + (f_.)*(x_)]), x_Symbol]
:> Dist[h/f, Int[Sqrt[e + f*x]/(Sqrt[a + b*x]*Sqrt[c + d*x]), x], x] + Dist[(f*g - e*h)/f, Int[1/(Sqrt[a + b*
x]*Sqrt[c + d*x]*Sqrt[e + f*x]), x], x] /; FreeQ[{a, b, c, d, e, f, g, h}, x] && SimplerQ[a + b*x, e + f*x] &&
SimplerQ[c + d*x, e + f*x]

Rubi steps

\begin {align*} \int \frac {\sqrt {1-2 x}}{(2+3 x)^{7/2} (3+5 x)^{5/2}} \, dx &=\frac {2 \sqrt {1-2 x}}{5 (2+3 x)^{5/2} (3+5 x)^{3/2}}-\frac {2}{5} \int \frac {-23+35 x}{\sqrt {1-2 x} (2+3 x)^{5/2} (3+5 x)^{5/2}} \, dx\\ &=\frac {2 \sqrt {1-2 x}}{5 (2+3 x)^{5/2} (3+5 x)^{3/2}}+\frac {556 \sqrt {1-2 x}}{105 (2+3 x)^{3/2} (3+5 x)^{3/2}}-\frac {4}{105} \int \frac {-\frac {5037}{2}+3475 x}{\sqrt {1-2 x} (2+3 x)^{3/2} (3+5 x)^{5/2}} \, dx\\ &=\frac {2 \sqrt {1-2 x}}{5 (2+3 x)^{5/2} (3+5 x)^{3/2}}+\frac {556 \sqrt {1-2 x}}{105 (2+3 x)^{3/2} (3+5 x)^{3/2}}+\frac {116044 \sqrt {1-2 x}}{735 \sqrt {2+3 x} (3+5 x)^{3/2}}-\frac {8}{735} \int \frac {-\frac {378705}{2}+\frac {435165 x}{2}}{\sqrt {1-2 x} \sqrt {2+3 x} (3+5 x)^{5/2}} \, dx\\ &=\frac {2 \sqrt {1-2 x}}{5 (2+3 x)^{5/2} (3+5 x)^{3/2}}+\frac {556 \sqrt {1-2 x}}{105 (2+3 x)^{3/2} (3+5 x)^{3/2}}+\frac {116044 \sqrt {1-2 x}}{735 \sqrt {2+3 x} (3+5 x)^{3/2}}-\frac {155104 \sqrt {1-2 x} \sqrt {2+3 x}}{147 (3+5 x)^{3/2}}+\frac {16 \int \frac {-\frac {31023465}{4}+4798530 x}{\sqrt {1-2 x} \sqrt {2+3 x} (3+5 x)^{3/2}} \, dx}{24255}\\ &=\frac {2 \sqrt {1-2 x}}{5 (2+3 x)^{5/2} (3+5 x)^{3/2}}+\frac {556 \sqrt {1-2 x}}{105 (2+3 x)^{3/2} (3+5 x)^{3/2}}+\frac {116044 \sqrt {1-2 x}}{735 \sqrt {2+3 x} (3+5 x)^{3/2}}-\frac {155104 \sqrt {1-2 x} \sqrt {2+3 x}}{147 (3+5 x)^{3/2}}+\frac {10312712 \sqrt {1-2 x} \sqrt {2+3 x}}{1617 \sqrt {3+5 x}}-\frac {32 \int \frac {-\frac {403972965}{4}-\frac {638099055 x}{4}}{\sqrt {1-2 x} \sqrt {2+3 x} \sqrt {3+5 x}} \, dx}{266805}\\ &=\frac {2 \sqrt {1-2 x}}{5 (2+3 x)^{5/2} (3+5 x)^{3/2}}+\frac {556 \sqrt {1-2 x}}{105 (2+3 x)^{3/2} (3+5 x)^{3/2}}+\frac {116044 \sqrt {1-2 x}}{735 \sqrt {2+3 x} (3+5 x)^{3/2}}-\frac {155104 \sqrt {1-2 x} \sqrt {2+3 x}}{147 (3+5 x)^{3/2}}+\frac {10312712 \sqrt {1-2 x} \sqrt {2+3 x}}{1617 \sqrt {3+5 x}}+\frac {155104}{245} \int \frac {1}{\sqrt {1-2 x} \sqrt {2+3 x} \sqrt {3+5 x}} \, dx+\frac {10312712 \int \frac {\sqrt {3+5 x}}{\sqrt {1-2 x} \sqrt {2+3 x}} \, dx}{2695}\\ &=\frac {2 \sqrt {1-2 x}}{5 (2+3 x)^{5/2} (3+5 x)^{3/2}}+\frac {556 \sqrt {1-2 x}}{105 (2+3 x)^{3/2} (3+5 x)^{3/2}}+\frac {116044 \sqrt {1-2 x}}{735 \sqrt {2+3 x} (3+5 x)^{3/2}}-\frac {155104 \sqrt {1-2 x} \sqrt {2+3 x}}{147 (3+5 x)^{3/2}}+\frac {10312712 \sqrt {1-2 x} \sqrt {2+3 x}}{1617 \sqrt {3+5 x}}-\frac {10312712 E\left (\sin ^{-1}\left (\sqrt {\frac {3}{7}} \sqrt {1-2 x}\right )|\frac {35}{33}\right )}{245 \sqrt {33}}-\frac {310208 F\left (\sin ^{-1}\left (\sqrt {\frac {3}{7}} \sqrt {1-2 x}\right )|\frac {35}{33}\right )}{245 \sqrt {33}}\\ \end {align*}

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Mathematica [A]
time = 4.66, size = 109, normalized size = 0.50 \begin {gather*} \frac {2 \left (\frac {\sqrt {1-2 x} \left (587237237+3669873602 x+8592783498 x^2+8934240060 x^3+3480540300 x^4\right )}{(2+3 x)^{5/2} (3+5 x)^{3/2}}+4 \sqrt {2} \left (1289089 E\left (\sin ^{-1}\left (\sqrt {\frac {2}{11}} \sqrt {3+5 x}\right )|-\frac {33}{2}\right )-649285 F\left (\sin ^{-1}\left (\sqrt {\frac {2}{11}} \sqrt {3+5 x}\right )|-\frac {33}{2}\right )\right )\right )}{8085} \end {gather*}

Antiderivative was successfully verified.

[In]

Integrate[Sqrt[1 - 2*x]/((2 + 3*x)^(7/2)*(3 + 5*x)^(5/2)),x]

[Out]

(2*((Sqrt[1 - 2*x]*(587237237 + 3669873602*x + 8592783498*x^2 + 8934240060*x^3 + 3480540300*x^4))/((2 + 3*x)^(
5/2)*(3 + 5*x)^(3/2)) + 4*Sqrt[2]*(1289089*EllipticE[ArcSin[Sqrt[2/11]*Sqrt[3 + 5*x]], -33/2] - 649285*Ellipti
cF[ArcSin[Sqrt[2/11]*Sqrt[3 + 5*x]], -33/2])))/8085

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Maple [B] Leaf count of result is larger than twice the leaf count of optimal. \(397\) vs. \(2(162)=324\).
time = 0.10, size = 398, normalized size = 1.83

method	result	size
elliptic	\(\frac {\sqrt {-\left (3+5 x \right ) \left (-1+2 x \right ) \left (2+3 x \right )}\, \left (-\frac {10 \sqrt {-30 x^{3}-23 x^{2}+7 x +6}}{3 \left (x +\frac {3}{5}\right )^{2}}+\frac {-\frac {182500}{11} x^{2}-\frac {91250}{33} x +\frac {182500}{33}}{\sqrt {\left (x +\frac {3}{5}\right ) \left (-30 x^{2}-5 x +10\right )}}+\frac {2 \sqrt {-30 x^{3}-23 x^{2}+7 x +6}}{15 \left (\frac {2}{3}+x \right )^{3}}+\frac {-\frac {1062084}{49} x^{2}-\frac {531042}{245} x +\frac {1593126}{245}}{\sqrt {\left (\frac {2}{3}+x \right ) \left (-30 x^{2}-3 x +9\right )}}+\frac {976 \sqrt {-30 x^{3}-23 x^{2}+7 x +6}}{105 \left (\frac {2}{3}+x \right )^{2}}+\frac {6528856 \sqrt {28+42 x}\, \sqrt {-15 x -9}\, \sqrt {21-42 x}\, \EllipticF \left (\frac {\sqrt {28+42 x}}{7}, \frac {\sqrt {70}}{2}\right )}{11319 \sqrt {-30 x^{3}-23 x^{2}+7 x +6}}+\frac {10312712 \sqrt {28+42 x}\, \sqrt {-15 x -9}\, \sqrt {21-42 x}\, \left (-\frac {\EllipticE \left (\frac {\sqrt {28+42 x}}{7}, \frac {\sqrt {70}}{2}\right )}{15}-\frac {3 \EllipticF \left (\frac {\sqrt {28+42 x}}{7}, \frac {\sqrt {70}}{2}\right )}{5}\right )}{11319 \sqrt {-30 x^{3}-23 x^{2}+7 x +6}}\right )}{\sqrt {1-2 x}\, \sqrt {2+3 x}\, \sqrt {3+5 x}}\)	\(301\)
default	\(-\frac {2 \sqrt {1-2 x}\, \left (115164720 \sqrt {2}\, \EllipticF \left (\frac {\sqrt {28+42 x}}{7}, \frac {\sqrt {70}}{2}\right ) x^{3} \sqrt {2+3 x}\, \sqrt {-3-5 x}\, \sqrt {1-2 x}-232036020 \sqrt {2}\, \EllipticE \left (\frac {\sqrt {28+42 x}}{7}, \frac {\sqrt {70}}{2}\right ) x^{3} \sqrt {2+3 x}\, \sqrt {-3-5 x}\, \sqrt {1-2 x}[phone] \sqrt {2}\, \EllipticF \left (\frac {\sqrt {28+42 x}}{7}, \frac {\sqrt {70}}{2}\right ) x^{2} \sqrt {2+3 x}\, \sqrt {-3-5 x}\, \sqrt {1-2 x}-448602972 \sqrt {2}\, \EllipticE \left (\frac {\sqrt {28+42 x}}{7}, \frac {\sqrt {70}}{2}\right ) x^{2} \sqrt {2+3 x}\, \sqrt {-3-5 x}\, \sqrt {1-2 x}[phone] \sqrt {2}\, \EllipticF \left (\frac {\sqrt {28+42 x}}{7}, \frac {\sqrt {70}}{2}\right ) x \sqrt {2+3 x}\, \sqrt {-3-5 x}\, \sqrt {1-2 x}-288755936 \sqrt {2}\, \EllipticE \left (\frac {\sqrt {28+42 x}}{7}, \frac {\sqrt {70}}{2}\right ) x \sqrt {2+3 x}\, \sqrt {-3-5 x}\, \sqrt {1-2 x}[phone] \sqrt {2}\, \sqrt {2+3 x}\, \sqrt {-3-5 x}\, \sqrt {1-2 x}\, \EllipticF \left (\frac {\sqrt {28+42 x}}{7}, \frac {\sqrt {70}}{2}\right )-61876272 \sqrt {2}\, \sqrt {2+3 x}\, \sqrt {-3-5 x}\, \sqrt {1-2 x}\, \EllipticE \left (\frac {\sqrt {28+42 x}}{7}, \frac {\sqrt {70}}{2}\right )-6961080600 x^{5}-14387939820 x^{4}-8251326936 x^{3}[phone] x^{2}[phone] x [phone]\right )}{8085 \left (2+3 x \right )^{\frac {5}{2}} \left (3+5 x \right )^{\frac {3}{2}} \left (-1+2 x \right )}\)	\(398\)

Verification of antiderivative is not currently implemented for this CAS.

[In]

int((1-2*x)^(1/2)/(2+3*x)^(7/2)/(3+5*x)^(5/2),x,method=_RETURNVERBOSE)

[Out]

-2/8085*(1-2*x)^(1/2)*(115164720*2^(1/2)*EllipticF(1/7*(28+42*x)^(1/2),1/2*70^(1/2))*x^3*(2+3*x)^(1/2)*(-3-5*x
)^(1/2)*(1-2*x)^(1/2)-232036020*2^(1/2)*EllipticE(1/7*(28+42*x)^(1/2),1/2*70^(1/2))*x^3*(2+3*x)^(1/2)*(-3-5*x)
^(1/2)*(1-2*x)^(1/2)[phone]*2^(1/2)*EllipticF(1/7*(28+42*x)^(1/2),1/2*70^(1/2))*x^2*(2+3*x)^(1/2)*(-3-5*x)^
(1/2)*(1-2*x)^(1/2)-448602972*2^(1/2)*EllipticE(1/7*(28+42*x)^(1/2),1/2*70^(1/2))*x^2*(2+3*x)^(1/2)*(-3-5*x)^(
1/2)*(1-2*x)^(1/2)[phone]*2^(1/2)*EllipticF(1/7*(28+42*x)^(1/2),1/2*70^(1/2))*x*(2+3*x)^(1/2)*(-3-5*x)^(1/2
)*(1-2*x)^(1/2)-288755936*2^(1/2)*EllipticE(1/7*(28+42*x)^(1/2),1/2*70^(1/2))*x*(2+3*x)^(1/2)*(-3-5*x)^(1/2)*(
1-2*x)^(1/2)[phone]*2^(1/2)*(2+3*x)^(1/2)*(-3-5*x)^(1/2)*(1-2*x)^(1/2)*EllipticF(1/7*(28+42*x)^(1/2),1/2*70^
(1/2))-61876272*2^(1/2)*(2+3*x)^(1/2)*(-3-5*x)^(1/2)*(1-2*x)^(1/2)*EllipticE(1/7*(28+42*x)^(1/2),1/2*70^(1/2))
-6961080600*x^5-14387939820*x^4-8251326936*x^3+1253036294*x^2+2495399128*x+587237237)/(2+3*x)^(5/2)/(3+5*x)^(3
/2)/(-1+2*x)

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Maxima [F]
time = 0.00, size = 0, normalized size = 0.00 \begin {gather*} \text {Failed to integrate} \end {gather*}

Verification of antiderivative is not currently implemented for this CAS.

[In]

integrate((1-2*x)^(1/2)/(2+3*x)^(7/2)/(3+5*x)^(5/2),x, algorithm="maxima")

[Out]

integrate(sqrt(-2*x + 1)/((5*x + 3)^(5/2)*(3*x + 2)^(7/2)), x)

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Fricas [A]
time = 0.29, size = 70, normalized size = 0.32 \begin {gather*} \frac {2 \, {\left (3480540300 \, x^{4} + 8934240060 \, x^{3} + 8592783498 \, x^{2} + 3669873602 \, x + 587237237\right )} \sqrt {5 \, x + 3} \sqrt {3 \, x + 2} \sqrt {-2 \, x + 1}}{8085 \, {\left (675 \, x^{5} + 2160 \, x^{4} + 2763 \, x^{3} + 1766 \, x^{2} + 564 \, x + 72\right )}} \end {gather*}

Verification of antiderivative is not currently implemented for this CAS.

[In]

integrate((1-2*x)^(1/2)/(2+3*x)^(7/2)/(3+5*x)^(5/2),x, algorithm="fricas")

[Out]

2/8085*(3480540300*x^4 + 8934240060*x^3 + 8592783498*x^2 + 3669873602*x + 587237237)*sqrt(5*x + 3)*sqrt(3*x +
2)*sqrt(-2*x + 1)/(675*x^5 + 2160*x^4 + 2763*x^3 + 1766*x^2 + 564*x + 72)

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Sympy [F(-2)]
time = 0.00, size = 0, normalized size = 0.00 \begin {gather*} \text {Exception raised: SystemError} \end {gather*}

Verification of antiderivative is not currently implemented for this CAS.

[In]

integrate((1-2*x)**(1/2)/(2+3*x)**(7/2)/(3+5*x)**(5/2),x)

[Out]

Exception raised: SystemError >> excessive stack use: stack is 4847 deep

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Giac [F]
time = 0.00, size = 0, normalized size = 0.00 \begin {gather*} \text {could not integrate} \end {gather*}

Verification of antiderivative is not currently implemented for this CAS.

[In]

integrate((1-2*x)^(1/2)/(2+3*x)^(7/2)/(3+5*x)^(5/2),x, algorithm="giac")

[Out]

integrate(sqrt(-2*x + 1)/((5*x + 3)^(5/2)*(3*x + 2)^(7/2)), x)

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Mupad [F]
time = 0.00, size = -1, normalized size = -0.00 \begin {gather*} \int \frac {\sqrt {1-2\,x}}{{\left (3\,x+2\right )}^{7/2}\,{\left (5\,x+3\right )}^{5/2}} \,d x \end {gather*}

Verification of antiderivative is not currently implemented for this CAS.

[In]

int((1 - 2*x)^(1/2)/((3*x + 2)^(7/2)*(5*x + 3)^(5/2)),x)

[Out]

int((1 - 2*x)^(1/2)/((3*x + 2)^(7/2)*(5*x + 3)^(5/2)), x)

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