3.20.29 \(\int \frac {1}{\sqrt {1-2 x} (2+3 x)^4 (3+5 x)^3} \, dx\)

Optimal. Leaf size=180 \[ \frac {137735775 \sqrt {1-2 x}}{83006 (5 x+3)}-\frac {2076675 \sqrt {1-2 x}}{7546 (5 x+3)^2}+\frac {12555 \sqrt {1-2 x}}{343 (3 x+2) (5 x+3)^2}+\frac {90 \sqrt {1-2 x}}{49 (3 x+2)^2 (5 x+3)^2}+\frac {\sqrt {1-2 x}}{7 (3 x+2)^3 (5 x+3)^2}+\frac {7852680}{343} \sqrt {\frac {3}{7}} \tanh ^{-1}\left (\sqrt {\frac {3}{7}} \sqrt {1-2 x}\right )-\frac {2689875}{121} \sqrt {\frac {5}{11}} \tanh ^{-1}\left (\sqrt {\frac {5}{11}} \sqrt {1-2 x}\right ) \]

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Rubi [A]  time = 0.07, antiderivative size = 180, normalized size of antiderivative = 1.00, number of steps used = 10, number of rules used = 5, integrand size = 24, \(\frac {\text {number of rules}}{\text {integrand size}}\) = 0.208, Rules used = {103, 151, 156, 63, 206} \begin {gather*} \frac {137735775 \sqrt {1-2 x}}{83006 (5 x+3)}-\frac {2076675 \sqrt {1-2 x}}{7546 (5 x+3)^2}+\frac {12555 \sqrt {1-2 x}}{343 (3 x+2) (5 x+3)^2}+\frac {90 \sqrt {1-2 x}}{49 (3 x+2)^2 (5 x+3)^2}+\frac {\sqrt {1-2 x}}{7 (3 x+2)^3 (5 x+3)^2}+\frac {7852680}{343} \sqrt {\frac {3}{7}} \tanh ^{-1}\left (\sqrt {\frac {3}{7}} \sqrt {1-2 x}\right )-\frac {2689875}{121} \sqrt {\frac {5}{11}} \tanh ^{-1}\left (\sqrt {\frac {5}{11}} \sqrt {1-2 x}\right ) \end {gather*}

Antiderivative was successfully verified.

[In]

Int[1/(Sqrt[1 - 2*x]*(2 + 3*x)^4*(3 + 5*x)^3),x]

[Out]

(-2076675*Sqrt[1 - 2*x])/(7546*(3 + 5*x)^2) + Sqrt[1 - 2*x]/(7*(2 + 3*x)^3*(3 + 5*x)^2) + (90*Sqrt[1 - 2*x])/(
49*(2 + 3*x)^2*(3 + 5*x)^2) + (12555*Sqrt[1 - 2*x])/(343*(2 + 3*x)*(3 + 5*x)^2) + (137735775*Sqrt[1 - 2*x])/(8
3006*(3 + 5*x)) + (7852680*Sqrt[3/7]*ArcTanh[Sqrt[3/7]*Sqrt[1 - 2*x]])/343 - (2689875*Sqrt[5/11]*ArcTanh[Sqrt[
5/11]*Sqrt[1 - 2*x]])/121

Rule 63

Int[((a_.) + (b_.)*(x_))^(m_)*((c_.) + (d_.)*(x_))^(n_), x_Symbol] :> With[{p = Denominator[m]}, Dist[p/b, Sub
st[Int[x^(p*(m + 1) - 1)*(c - (a*d)/b + (d*x^p)/b)^n, x], x, (a + b*x)^(1/p)], x]] /; FreeQ[{a, b, c, d}, x] &
& NeQ[b*c - a*d, 0] && LtQ[-1, m, 0] && LeQ[-1, n, 0] && LeQ[Denominator[n], Denominator[m]] && IntLinearQ[a,
b, c, d, m, n, x]

Rule 103

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

Rule 151

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] && IntegerQ[m]

Rule 156

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

Rule 206

Int[((a_) + (b_.)*(x_)^2)^(-1), x_Symbol] :> Simp[(1*ArcTanh[(Rt[-b, 2]*x)/Rt[a, 2]])/(Rt[a, 2]*Rt[-b, 2]), x]
/; FreeQ[{a, b}, x] && NegQ[a/b] && (GtQ[a, 0] || LtQ[b, 0])

Rubi steps

\begin {align*} \int \frac {1}{\sqrt {1-2 x} (2+3 x)^4 (3+5 x)^3} \, dx &=\frac {\sqrt {1-2 x}}{7 (2+3 x)^3 (3+5 x)^2}+\frac {1}{21} \int \frac {90-135 x}{\sqrt {1-2 x} (2+3 x)^3 (3+5 x)^3} \, dx\\ &=\frac {\sqrt {1-2 x}}{7 (2+3 x)^3 (3+5 x)^2}+\frac {90 \sqrt {1-2 x}}{49 (2+3 x)^2 (3+5 x)^2}+\frac {1}{294} \int \frac {12510-18900 x}{\sqrt {1-2 x} (2+3 x)^2 (3+5 x)^3} \, dx\\ &=\frac {\sqrt {1-2 x}}{7 (2+3 x)^3 (3+5 x)^2}+\frac {90 \sqrt {1-2 x}}{49 (2+3 x)^2 (3+5 x)^2}+\frac {12555 \sqrt {1-2 x}}{343 (2+3 x) (3+5 x)^2}+\frac {\int \frac {1362060-1883250 x}{\sqrt {1-2 x} (2+3 x) (3+5 x)^3} \, dx}{2058}\\ &=-\frac {2076675 \sqrt {1-2 x}}{7546 (3+5 x)^2}+\frac {\sqrt {1-2 x}}{7 (2+3 x)^3 (3+5 x)^2}+\frac {90 \sqrt {1-2 x}}{49 (2+3 x)^2 (3+5 x)^2}+\frac {12555 \sqrt {1-2 x}}{343 (2+3 x) (3+5 x)^2}-\frac {\int \frac {97998660-112140450 x}{\sqrt {1-2 x} (2+3 x) (3+5 x)^2} \, dx}{45276}\\ &=-\frac {2076675 \sqrt {1-2 x}}{7546 (3+5 x)^2}+\frac {\sqrt {1-2 x}}{7 (2+3 x)^3 (3+5 x)^2}+\frac {90 \sqrt {1-2 x}}{49 (2+3 x)^2 (3+5 x)^2}+\frac {12555 \sqrt {1-2 x}}{343 (2+3 x) (3+5 x)^2}+\frac {137735775 \sqrt {1-2 x}}{83006 (3+5 x)}+\frac {\int \frac {4048216380-2479243950 x}{\sqrt {1-2 x} (2+3 x) (3+5 x)} \, dx}{498036}\\ &=-\frac {2076675 \sqrt {1-2 x}}{7546 (3+5 x)^2}+\frac {\sqrt {1-2 x}}{7 (2+3 x)^3 (3+5 x)^2}+\frac {90 \sqrt {1-2 x}}{49 (2+3 x)^2 (3+5 x)^2}+\frac {12555 \sqrt {1-2 x}}{343 (2+3 x) (3+5 x)^2}+\frac {137735775 \sqrt {1-2 x}}{83006 (3+5 x)}-\frac {11779020}{343} \int \frac {1}{\sqrt {1-2 x} (2+3 x)} \, dx+\frac {13449375}{242} \int \frac {1}{\sqrt {1-2 x} (3+5 x)} \, dx\\ &=-\frac {2076675 \sqrt {1-2 x}}{7546 (3+5 x)^2}+\frac {\sqrt {1-2 x}}{7 (2+3 x)^3 (3+5 x)^2}+\frac {90 \sqrt {1-2 x}}{49 (2+3 x)^2 (3+5 x)^2}+\frac {12555 \sqrt {1-2 x}}{343 (2+3 x) (3+5 x)^2}+\frac {137735775 \sqrt {1-2 x}}{83006 (3+5 x)}+\frac {11779020}{343} \operatorname {Subst}\left (\int \frac {1}{\frac {7}{2}-\frac {3 x^2}{2}} \, dx,x,\sqrt {1-2 x}\right )-\frac {13449375}{242} \operatorname {Subst}\left (\int \frac {1}{\frac {11}{2}-\frac {5 x^2}{2}} \, dx,x,\sqrt {1-2 x}\right )\\ &=-\frac {2076675 \sqrt {1-2 x}}{7546 (3+5 x)^2}+\frac {\sqrt {1-2 x}}{7 (2+3 x)^3 (3+5 x)^2}+\frac {90 \sqrt {1-2 x}}{49 (2+3 x)^2 (3+5 x)^2}+\frac {12555 \sqrt {1-2 x}}{343 (2+3 x) (3+5 x)^2}+\frac {137735775 \sqrt {1-2 x}}{83006 (3+5 x)}+\frac {7852680}{343} \sqrt {\frac {3}{7}} \tanh ^{-1}\left (\sqrt {\frac {3}{7}} \sqrt {1-2 x}\right )-\frac {2689875}{121} \sqrt {\frac {5}{11}} \tanh ^{-1}\left (\sqrt {\frac {5}{11}} \sqrt {1-2 x}\right )\\ \end {align*}

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Mathematica [A]  time = 0.14, size = 106, normalized size = 0.59 \begin {gather*} \frac {\sqrt {1-2 x} \left (18594329625 x^4+47728484550 x^3+45899434890 x^2+19599448500 x+3135381218\right )}{83006 (3 x+2)^3 (5 x+3)^2}+\frac {7852680}{343} \sqrt {\frac {3}{7}} \tanh ^{-1}\left (\sqrt {\frac {3}{7}} \sqrt {1-2 x}\right )-\frac {2689875}{121} \sqrt {\frac {5}{11}} \tanh ^{-1}\left (\sqrt {\frac {5}{11}} \sqrt {1-2 x}\right ) \end {gather*}

Antiderivative was successfully verified.

[In]

Integrate[1/(Sqrt[1 - 2*x]*(2 + 3*x)^4*(3 + 5*x)^3),x]

[Out]

(Sqrt[1 - 2*x]*(3135381218 + 19599448500*x + 45899434890*x^2 + 47728484550*x^3 + 18594329625*x^4))/(83006*(2 +
3*x)^3*(3 + 5*x)^2) + (7852680*Sqrt[3/7]*ArcTanh[Sqrt[3/7]*Sqrt[1 - 2*x]])/343 - (2689875*Sqrt[5/11]*ArcTanh[
Sqrt[5/11]*Sqrt[1 - 2*x]])/121

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IntegrateAlgebraic [A]  time = 0.41, size = 141, normalized size = 0.78 \begin {gather*} \frac {-18594329625 (1-2 x)^{9/2}[phone] (1-2 x)^{7/2}-581534624610 (1-2 x)^{5/2}[phone] (1-2 x)^{3/2}-504610725773 \sqrt {1-2 x}}{41503 (3 (1-2 x)-7)^3 (5 (1-2 x)-11)^2}+\frac {7852680}{343} \sqrt {\frac {3}{7}} \tanh ^{-1}\left (\sqrt {\frac {3}{7}} \sqrt {1-2 x}\right )-\frac {2689875}{121} \sqrt {\frac {5}{11}} \tanh ^{-1}\left (\sqrt {\frac {5}{11}} \sqrt {1-2 x}\right ) \end {gather*}

Antiderivative was successfully verified.

[In]

IntegrateAlgebraic[1/(Sqrt[1 - 2*x]*(2 + 3*x)^4*(3 + 5*x)^3),x]

[Out]

(-504610725773*Sqrt[1 - 2*x] + 884739292920*(1 - 2*x)^(3/2) - 581534624610*(1 - 2*x)^(5/2) + 169834287600*(1 -
2*x)^(7/2) - 18594329625*(1 - 2*x)^(9/2))/(41503*(-7 + 3*(1 - 2*x))^3*(-11 + 5*(1 - 2*x))^2) + (7852680*Sqrt[
3/7]*ArcTanh[Sqrt[3/7]*Sqrt[1 - 2*x]])/343 - (2689875*Sqrt[5/11]*ArcTanh[Sqrt[5/11]*Sqrt[1 - 2*x]])/121

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fricas [A]  time = 1.56, size = 182, normalized size = 1.01 \begin {gather*} \frac {6458389875 \, \sqrt {11} \sqrt {5} {\left (675 \, x^{5} + 2160 \, x^{4} + 2763 \, x^{3} + 1766 \, x^{2} + 564 \, x + 72\right )} \log \left (\frac {\sqrt {11} \sqrt {5} \sqrt {-2 \, x + 1} + 5 \, x - 8}{5 \, x + 3}\right ) + 10451917080 \, \sqrt {7} \sqrt {3} {\left (675 \, x^{5} + 2160 \, x^{4} + 2763 \, x^{3} + 1766 \, x^{2} + 564 \, x + 72\right )} \log \left (-\frac {\sqrt {7} \sqrt {3} \sqrt {-2 \, x + 1} - 3 \, x + 5}{3 \, x + 2}\right ) + 77 \, {\left (18594329625 \, x^{4} + 47728484550 \, x^{3} + 45899434890 \, x^{2} + 19599448500 \, x + 3135381218\right )} \sqrt {-2 \, x + 1}}{6391462 \, {\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+3*x)^4/(3+5*x)^3/(1-2*x)^(1/2),x, algorithm="fricas")

[Out]

1/6391462*(6458389875*sqrt(11)*sqrt(5)*(675*x^5 + 2160*x^4 + 2763*x^3 + 1766*x^2 + 564*x + 72)*log((sqrt(11)*s
qrt(5)*sqrt(-2*x + 1) + 5*x - 8)/(5*x + 3)) + 10451917080*sqrt(7)*sqrt(3)*(675*x^5 + 2160*x^4 + 2763*x^3 + 176
6*x^2 + 564*x + 72)*log(-(sqrt(7)*sqrt(3)*sqrt(-2*x + 1) - 3*x + 5)/(3*x + 2)) + 77*(18594329625*x^4 + 4772848
4550*x^3 + 45899434890*x^2 + 19599448500*x + 3135381218)*sqrt(-2*x + 1))/(675*x^5 + 2160*x^4 + 2763*x^3 + 1766
*x^2 + 564*x + 72)

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giac [A]  time = 1.24, size = 151, normalized size = 0.84 \begin {gather*} \frac {2689875}{2662} \, \sqrt {55} \log \left (\frac {{\left | -2 \, \sqrt {55} + 10 \, \sqrt {-2 \, x + 1} \right |}}{2 \, {\left (\sqrt {55} + 5 \, \sqrt {-2 \, x + 1}\right )}}\right ) - \frac {3926340}{2401} \, \sqrt {21} \log \left (\frac {{\left | -2 \, \sqrt {21} + 6 \, \sqrt {-2 \, x + 1} \right |}}{2 \, {\left (\sqrt {21} + 3 \, \sqrt {-2 \, x + 1}\right )}}\right ) - \frac {625 \, {\left (1305 \, {\left (-2 \, x + 1\right )}^{\frac {3}{2}} - 2849 \, \sqrt {-2 \, x + 1}\right )}}{484 \, {\left (5 \, x + 3\right )}^{2}} + \frac {27 \, {\left (33795 \, {\left (2 \, x - 1\right )}^{2} \sqrt {-2 \, x + 1} - 158830 \, {\left (-2 \, x + 1\right )}^{\frac {3}{2}} + 186641 \, \sqrt {-2 \, x + 1}\right )}}{686 \, {\left (3 \, x + 2\right )}^{3}} \end {gather*}

Verification of antiderivative is not currently implemented for this CAS.

[In]

integrate(1/(2+3*x)^4/(3+5*x)^3/(1-2*x)^(1/2),x, algorithm="giac")

[Out]

2689875/2662*sqrt(55)*log(1/2*abs(-2*sqrt(55) + 10*sqrt(-2*x + 1))/(sqrt(55) + 5*sqrt(-2*x + 1))) - 3926340/24
01*sqrt(21)*log(1/2*abs(-2*sqrt(21) + 6*sqrt(-2*x + 1))/(sqrt(21) + 3*sqrt(-2*x + 1))) - 625/484*(1305*(-2*x +
1)^(3/2) - 2849*sqrt(-2*x + 1))/(5*x + 3)^2 + 27/686*(33795*(2*x - 1)^2*sqrt(-2*x + 1) - 158830*(-2*x + 1)^(3
/2) + 186641*sqrt(-2*x + 1))/(3*x + 2)^3

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maple [A]  time = 0.01, size = 103, normalized size = 0.57 \begin {gather*} \frac {7852680 \sqrt {21}\, \arctanh \left (\frac {\sqrt {21}\, \sqrt {-2 x +1}}{7}\right )}{2401}-\frac {2689875 \sqrt {55}\, \arctanh \left (\frac {\sqrt {55}\, \sqrt {-2 x +1}}{11}\right )}{1331}+\frac {-\frac {815625 \left (-2 x +1\right )^{\frac {3}{2}}}{121}+\frac {161875 \sqrt {-2 x +1}}{11}}{\left (-10 x -6\right )^{2}}-\frac {2916 \left (\frac {3755 \left (-2 x +1\right )^{\frac {5}{2}}}{1029}-\frac {22690 \left (-2 x +1\right )^{\frac {3}{2}}}{1323}+\frac {3809 \sqrt {-2 x +1}}{189}\right )}{\left (-6 x -4\right )^{3}} \end {gather*}

Verification of antiderivative is not currently implemented for this CAS.

[In]

int(1/(3*x+2)^4/(5*x+3)^3/(-2*x+1)^(1/2),x)

[Out]

312500*(-261/12100*(-2*x+1)^(3/2)+259/5500*(-2*x+1)^(1/2))/(-10*x-6)^2-2689875/1331*arctanh(1/11*55^(1/2)*(-2*
x+1)^(1/2))*55^(1/2)-2916*(3755/1029*(-2*x+1)^(5/2)-22690/1323*(-2*x+1)^(3/2)+3809/189*(-2*x+1)^(1/2))/(-6*x-4
)^3+7852680/2401*arctanh(1/7*21^(1/2)*(-2*x+1)^(1/2))*21^(1/2)

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maxima [A]  time = 1.41, size = 164, normalized size = 0.91 \begin {gather*} \frac {2689875}{2662} \, \sqrt {55} \log \left (-\frac {\sqrt {55} - 5 \, \sqrt {-2 \, x + 1}}{\sqrt {55} + 5 \, \sqrt {-2 \, x + 1}}\right ) - \frac {3926340}{2401} \, \sqrt {21} \log \left (-\frac {\sqrt {21} - 3 \, \sqrt {-2 \, x + 1}}{\sqrt {21} + 3 \, \sqrt {-2 \, x + 1}}\right ) + \frac {18594329625 \, {\left (-2 \, x + 1\right )}^{\frac {9}{2}} - 169834287600 \, {\left (-2 \, x + 1\right )}^{\frac {7}{2}} + 581534624610 \, {\left (-2 \, x + 1\right )}^{\frac {5}{2}} - 884739292920 \, {\left (-2 \, x + 1\right )}^{\frac {3}{2}} + 504610725773 \, \sqrt {-2 \, x + 1}}{41503 \, {\left (675 \, {\left (2 \, x - 1\right )}^{5} + 7695 \, {\left (2 \, x - 1\right )}^{4} + 35082 \, {\left (2 \, x - 1\right )}^{3} + 79954 \, {\left (2 \, x - 1\right )}^{2} + 182182 \, x - 49588\right )}} \end {gather*}

Verification of antiderivative is not currently implemented for this CAS.

[In]

integrate(1/(2+3*x)^4/(3+5*x)^3/(1-2*x)^(1/2),x, algorithm="maxima")

[Out]

2689875/2662*sqrt(55)*log(-(sqrt(55) - 5*sqrt(-2*x + 1))/(sqrt(55) + 5*sqrt(-2*x + 1))) - 3926340/2401*sqrt(21
)*log(-(sqrt(21) - 3*sqrt(-2*x + 1))/(sqrt(21) + 3*sqrt(-2*x + 1))) + 1/41503*(18594329625*(-2*x + 1)^(9/2) -
169834287600*(-2*x + 1)^(7/2) + 581534624610*(-2*x + 1)^(5/2) - 884739292920*(-2*x + 1)^(3/2) + 504610725773*s
qrt(-2*x + 1))/(675*(2*x - 1)^5 + 7695*(2*x - 1)^4 + 35082*(2*x - 1)^3 + 79954*(2*x - 1)^2 + 182182*x - 49588)

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mupad [B]  time = 1.29, size = 125, normalized size = 0.69 \begin {gather*} \frac {\frac {936198007\,\sqrt {1-2\,x}}{51975}-\frac {936232056\,{\left (1-2\,x\right )}^{3/2}}{29645}+\frac {4307663886\,{\left (1-2\,x\right )}^{5/2}}{207515}-\frac {251606352\,{\left (1-2\,x\right )}^{7/2}}{41503}+\frac {27547155\,{\left (1-2\,x\right )}^{9/2}}{41503}}{\frac {182182\,x}{675}+\frac {79954\,{\left (2\,x-1\right )}^2}{675}+\frac {3898\,{\left (2\,x-1\right )}^3}{75}+\frac {57\,{\left (2\,x-1\right )}^4}{5}+{\left (2\,x-1\right )}^5-\frac {49588}{675}}+\frac {7852680\,\sqrt {21}\,\mathrm {atanh}\left (\frac {\sqrt {21}\,\sqrt {1-2\,x}}{7}\right )}{2401}-\frac {2689875\,\sqrt {55}\,\mathrm {atanh}\left (\frac {\sqrt {55}\,\sqrt {1-2\,x}}{11}\right )}{1331} \end {gather*}

Verification of antiderivative is not currently implemented for this CAS.

[In]

int(1/((1 - 2*x)^(1/2)*(3*x + 2)^4*(5*x + 3)^3),x)

[Out]

((936198007*(1 - 2*x)^(1/2))/51975 - (936232056*(1 - 2*x)^(3/2))/29645 + (4307663886*(1 - 2*x)^(5/2))/207515 -
(251606352*(1 - 2*x)^(7/2))/41503 + (27547155*(1 - 2*x)^(9/2))/41503)/((182182*x)/675 + (79954*(2*x - 1)^2)/6
75 + (3898*(2*x - 1)^3)/75 + (57*(2*x - 1)^4)/5 + (2*x - 1)^5 - 49588/675) + (7852680*21^(1/2)*atanh((21^(1/2)
*(1 - 2*x)^(1/2))/7))/2401 - (2689875*55^(1/2)*atanh((55^(1/2)*(1 - 2*x)^(1/2))/11))/1331

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sympy [F(-1)]  time = 0.00, size = 0, normalized size = 0.00 \begin {gather*} \text {Timed out} \end {gather*}

Verification of antiderivative is not currently implemented for this CAS.

[In]

integrate(1/(2+3*x)**4/(3+5*x)**3/(1-2*x)**(1/2),x)

[Out]

Timed out

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