3.21.22 \(\int \frac {(a+b x+c x^2)^{3/2}}{(d+e x)^7} \, dx\)

Optimal. Leaf size=409 \[ \frac {\left (a+b x+c x^2\right )^{3/2} \left (-4 c e (a e+6 b d)+7 b^2 e^2+24 c^2 d^2\right ) (-2 a e+x (2 c d-b e)+b d)}{192 (d+e x)^4 \left (a e^2-b d e+c d^2\right )^3}-\frac {\left (b^2-4 a c\right ) \sqrt {a+b x+c x^2} \left (-4 c e (a e+6 b d)+7 b^2 e^2+24 c^2 d^2\right ) (-2 a e+x (2 c d-b e)+b d)}{512 (d+e x)^2 \left (a e^2-b d e+c d^2\right )^4}+\frac {\left (b^2-4 a c\right )^2 \left (-4 c e (a e+6 b d)+7 b^2 e^2+24 c^2 d^2\right ) \tanh ^{-1}\left (\frac {-2 a e+x (2 c d-b e)+b d}{2 \sqrt {a+b x+c x^2} \sqrt {a e^2-b d e+c d^2}}\right )}{1024 \left (a e^2-b d e+c d^2\right )^{9/2}}-\frac {7 e \left (a+b x+c x^2\right )^{5/2} (2 c d-b e)}{60 (d+e x)^5 \left (a e^2-b d e+c d^2\right )^2}-\frac {e \left (a+b x+c x^2\right )^{5/2}}{6 (d+e x)^6 \left (a e^2-b d e+c d^2\right )} \]

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Rubi [A]  time = 0.60, antiderivative size = 409, normalized size of antiderivative = 1.00, number of steps used = 6, number of rules used = 5, integrand size = 22, \(\frac {\text {number of rules}}{\text {integrand size}}\) = 0.227, Rules used = {744, 806, 720, 724, 206} \begin {gather*} \frac {\left (a+b x+c x^2\right )^{3/2} \left (-4 c e (a e+6 b d)+7 b^2 e^2+24 c^2 d^2\right ) (-2 a e+x (2 c d-b e)+b d)}{192 (d+e x)^4 \left (a e^2-b d e+c d^2\right )^3}-\frac {\left (b^2-4 a c\right ) \sqrt {a+b x+c x^2} \left (-4 c e (a e+6 b d)+7 b^2 e^2+24 c^2 d^2\right ) (-2 a e+x (2 c d-b e)+b d)}{512 (d+e x)^2 \left (a e^2-b d e+c d^2\right )^4}+\frac {\left (b^2-4 a c\right )^2 \left (-4 c e (a e+6 b d)+7 b^2 e^2+24 c^2 d^2\right ) \tanh ^{-1}\left (\frac {-2 a e+x (2 c d-b e)+b d}{2 \sqrt {a+b x+c x^2} \sqrt {a e^2-b d e+c d^2}}\right )}{1024 \left (a e^2-b d e+c d^2\right )^{9/2}}-\frac {7 e \left (a+b x+c x^2\right )^{5/2} (2 c d-b e)}{60 (d+e x)^5 \left (a e^2-b d e+c d^2\right )^2}-\frac {e \left (a+b x+c x^2\right )^{5/2}}{6 (d+e x)^6 \left (a e^2-b d e+c d^2\right )} \end {gather*}

Antiderivative was successfully verified.

[In]

Int[(a + b*x + c*x^2)^(3/2)/(d + e*x)^7,x]

[Out]

-((b^2 - 4*a*c)*(24*c^2*d^2 + 7*b^2*e^2 - 4*c*e*(6*b*d + a*e))*(b*d - 2*a*e + (2*c*d - b*e)*x)*Sqrt[a + b*x +
c*x^2])/(512*(c*d^2 - b*d*e + a*e^2)^4*(d + e*x)^2) + ((24*c^2*d^2 + 7*b^2*e^2 - 4*c*e*(6*b*d + a*e))*(b*d - 2
*a*e + (2*c*d - b*e)*x)*(a + b*x + c*x^2)^(3/2))/(192*(c*d^2 - b*d*e + a*e^2)^3*(d + e*x)^4) - (e*(a + b*x + c
*x^2)^(5/2))/(6*(c*d^2 - b*d*e + a*e^2)*(d + e*x)^6) - (7*e*(2*c*d - b*e)*(a + b*x + c*x^2)^(5/2))/(60*(c*d^2
- b*d*e + a*e^2)^2*(d + e*x)^5) + ((b^2 - 4*a*c)^2*(24*c^2*d^2 + 7*b^2*e^2 - 4*c*e*(6*b*d + a*e))*ArcTanh[(b*d
- 2*a*e + (2*c*d - b*e)*x)/(2*Sqrt[c*d^2 - b*d*e + a*e^2]*Sqrt[a + b*x + c*x^2])])/(1024*(c*d^2 - b*d*e + a*e
^2)^(9/2))

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])

Rule 720

Int[((d_.) + (e_.)*(x_))^(m_)*((a_.) + (b_.)*(x_) + (c_.)*(x_)^2)^(p_), x_Symbol] :> -Simp[((d + e*x)^(m + 1)*
(d*b - 2*a*e + (2*c*d - b*e)*x)*(a + b*x + c*x^2)^p)/(2*(m + 1)*(c*d^2 - b*d*e + a*e^2)), x] + Dist[(p*(b^2 -
4*a*c))/(2*(m + 1)*(c*d^2 - b*d*e + a*e^2)), Int[(d + e*x)^(m + 2)*(a + b*x + c*x^2)^(p - 1), x], x] /; FreeQ[
{a, b, c, d, e}, x] && NeQ[b^2 - 4*a*c, 0] && NeQ[c*d^2 - b*d*e + a*e^2, 0] && NeQ[2*c*d - b*e, 0] && EqQ[m +
2*p + 2, 0] && GtQ[p, 0]

Rule 724

Int[1/(((d_.) + (e_.)*(x_))*Sqrt[(a_.) + (b_.)*(x_) + (c_.)*(x_)^2]), x_Symbol] :> Dist[-2, Subst[Int[1/(4*c*d
^2 - 4*b*d*e + 4*a*e^2 - x^2), x], x, (2*a*e - b*d - (2*c*d - b*e)*x)/Sqrt[a + b*x + c*x^2]], x] /; FreeQ[{a,
b, c, d, e}, x] && NeQ[b^2 - 4*a*c, 0] && NeQ[2*c*d - b*e, 0]

Rule 744

Int[((d_.) + (e_.)*(x_))^(m_)*((a_.) + (b_.)*(x_) + (c_.)*(x_)^2)^(p_), x_Symbol] :> Simp[(e*(d + e*x)^(m + 1)
*(a + b*x + c*x^2)^(p + 1))/((m + 1)*(c*d^2 - b*d*e + a*e^2)), x] + Dist[1/((m + 1)*(c*d^2 - b*d*e + a*e^2)),
Int[(d + e*x)^(m + 1)*Simp[c*d*(m + 1) - b*e*(m + p + 2) - c*e*(m + 2*p + 3)*x, x]*(a + b*x + c*x^2)^p, x], x]
/; FreeQ[{a, b, c, d, e, m, p}, x] && NeQ[b^2 - 4*a*c, 0] && NeQ[c*d^2 - b*d*e + a*e^2, 0] && NeQ[2*c*d - b*e
, 0] && NeQ[m, -1] && ((LtQ[m, -1] && IntQuadraticQ[a, b, c, d, e, m, p, x]) || (SumSimplerQ[m, 1] && IntegerQ
[p]) || ILtQ[Simplify[m + 2*p + 3], 0])

Rule 806

Int[((d_.) + (e_.)*(x_))^(m_)*((f_.) + (g_.)*(x_))*((a_.) + (b_.)*(x_) + (c_.)*(x_)^2)^(p_.), x_Symbol] :> -Si
mp[((e*f - d*g)*(d + e*x)^(m + 1)*(a + b*x + c*x^2)^(p + 1))/(2*(p + 1)*(c*d^2 - b*d*e + a*e^2)), x] - Dist[(b
*(e*f + d*g) - 2*(c*d*f + a*e*g))/(2*(c*d^2 - b*d*e + a*e^2)), Int[(d + e*x)^(m + 1)*(a + b*x + c*x^2)^p, x],
x] /; FreeQ[{a, b, c, d, e, f, g, m, p}, x] && NeQ[b^2 - 4*a*c, 0] && NeQ[c*d^2 - b*d*e + a*e^2, 0] && EqQ[Sim
plify[m + 2*p + 3], 0]

Rubi steps

\begin {align*} \int \frac {\left (a+b x+c x^2\right )^{3/2}}{(d+e x)^7} \, dx &=-\frac {e \left (a+b x+c x^2\right )^{5/2}}{6 \left (c d^2-b d e+a e^2\right ) (d+e x)^6}-\frac {\int \frac {\left (\frac {1}{2} (-12 c d+7 b e)+c e x\right ) \left (a+b x+c x^2\right )^{3/2}}{(d+e x)^6} \, dx}{6 \left (c d^2-b d e+a e^2\right )}\\ &=-\frac {e \left (a+b x+c x^2\right )^{5/2}}{6 \left (c d^2-b d e+a e^2\right ) (d+e x)^6}-\frac {7 e (2 c d-b e) \left (a+b x+c x^2\right )^{5/2}}{60 \left (c d^2-b d e+a e^2\right )^2 (d+e x)^5}+\frac {\left (24 c^2 d^2+7 b^2 e^2-4 c e (6 b d+a e)\right ) \int \frac {\left (a+b x+c x^2\right )^{3/2}}{(d+e x)^5} \, dx}{24 \left (c d^2-b d e+a e^2\right )^2}\\ &=\frac {\left (24 c^2 d^2+7 b^2 e^2-4 c e (6 b d+a e)\right ) (b d-2 a e+(2 c d-b e) x) \left (a+b x+c x^2\right )^{3/2}}{192 \left (c d^2-b d e+a e^2\right )^3 (d+e x)^4}-\frac {e \left (a+b x+c x^2\right )^{5/2}}{6 \left (c d^2-b d e+a e^2\right ) (d+e x)^6}-\frac {7 e (2 c d-b e) \left (a+b x+c x^2\right )^{5/2}}{60 \left (c d^2-b d e+a e^2\right )^2 (d+e x)^5}-\frac {\left (\left (b^2-4 a c\right ) \left (24 c^2 d^2+7 b^2 e^2-4 c e (6 b d+a e)\right )\right ) \int \frac {\sqrt {a+b x+c x^2}}{(d+e x)^3} \, dx}{128 \left (c d^2-b d e+a e^2\right )^3}\\ &=-\frac {\left (b^2-4 a c\right ) \left (24 c^2 d^2+7 b^2 e^2-4 c e (6 b d+a e)\right ) (b d-2 a e+(2 c d-b e) x) \sqrt {a+b x+c x^2}}{512 \left (c d^2-b d e+a e^2\right )^4 (d+e x)^2}+\frac {\left (24 c^2 d^2+7 b^2 e^2-4 c e (6 b d+a e)\right ) (b d-2 a e+(2 c d-b e) x) \left (a+b x+c x^2\right )^{3/2}}{192 \left (c d^2-b d e+a e^2\right )^3 (d+e x)^4}-\frac {e \left (a+b x+c x^2\right )^{5/2}}{6 \left (c d^2-b d e+a e^2\right ) (d+e x)^6}-\frac {7 e (2 c d-b e) \left (a+b x+c x^2\right )^{5/2}}{60 \left (c d^2-b d e+a e^2\right )^2 (d+e x)^5}+\frac {\left (\left (b^2-4 a c\right )^2 \left (24 c^2 d^2+7 b^2 e^2-4 c e (6 b d+a e)\right )\right ) \int \frac {1}{(d+e x) \sqrt {a+b x+c x^2}} \, dx}{1024 \left (c d^2-b d e+a e^2\right )^4}\\ &=-\frac {\left (b^2-4 a c\right ) \left (24 c^2 d^2+7 b^2 e^2-4 c e (6 b d+a e)\right ) (b d-2 a e+(2 c d-b e) x) \sqrt {a+b x+c x^2}}{512 \left (c d^2-b d e+a e^2\right )^4 (d+e x)^2}+\frac {\left (24 c^2 d^2+7 b^2 e^2-4 c e (6 b d+a e)\right ) (b d-2 a e+(2 c d-b e) x) \left (a+b x+c x^2\right )^{3/2}}{192 \left (c d^2-b d e+a e^2\right )^3 (d+e x)^4}-\frac {e \left (a+b x+c x^2\right )^{5/2}}{6 \left (c d^2-b d e+a e^2\right ) (d+e x)^6}-\frac {7 e (2 c d-b e) \left (a+b x+c x^2\right )^{5/2}}{60 \left (c d^2-b d e+a e^2\right )^2 (d+e x)^5}-\frac {\left (\left (b^2-4 a c\right )^2 \left (24 c^2 d^2+7 b^2 e^2-4 c e (6 b d+a e)\right )\right ) \operatorname {Subst}\left (\int \frac {1}{4 c d^2-4 b d e+4 a e^2-x^2} \, dx,x,\frac {-b d+2 a e-(2 c d-b e) x}{\sqrt {a+b x+c x^2}}\right )}{512 \left (c d^2-b d e+a e^2\right )^4}\\ &=-\frac {\left (b^2-4 a c\right ) \left (24 c^2 d^2+7 b^2 e^2-4 c e (6 b d+a e)\right ) (b d-2 a e+(2 c d-b e) x) \sqrt {a+b x+c x^2}}{512 \left (c d^2-b d e+a e^2\right )^4 (d+e x)^2}+\frac {\left (24 c^2 d^2+7 b^2 e^2-4 c e (6 b d+a e)\right ) (b d-2 a e+(2 c d-b e) x) \left (a+b x+c x^2\right )^{3/2}}{192 \left (c d^2-b d e+a e^2\right )^3 (d+e x)^4}-\frac {e \left (a+b x+c x^2\right )^{5/2}}{6 \left (c d^2-b d e+a e^2\right ) (d+e x)^6}-\frac {7 e (2 c d-b e) \left (a+b x+c x^2\right )^{5/2}}{60 \left (c d^2-b d e+a e^2\right )^2 (d+e x)^5}+\frac {\left (b^2-4 a c\right )^2 \left (24 c^2 d^2+7 b^2 e^2-4 c e (6 b d+a e)\right ) \tanh ^{-1}\left (\frac {b d-2 a e+(2 c d-b e) x}{2 \sqrt {c d^2-b d e+a e^2} \sqrt {a+b x+c x^2}}\right )}{1024 \left (c d^2-b d e+a e^2\right )^{9/2}}\\ \end {align*}

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Mathematica [A]  time = 1.69, size = 349, normalized size = 0.85 \begin {gather*} -\frac {\left (-2 c e (a e+6 b d)+\frac {7 b^2 e^2}{2}+12 c^2 d^2\right ) \left (3 \left (b^2-4 a c\right ) \left (\frac {\left (b^2-4 a c\right ) \tanh ^{-1}\left (\frac {2 a e-b d+b e x-2 c d x}{2 \sqrt {a+x (b+c x)} \sqrt {e (a e-b d)+c d^2}}\right )}{8 \left (e (a e-b d)+c d^2\right )^{3/2}}+\frac {\sqrt {a+x (b+c x)} (-2 a e+b (d-e x)+2 c d x)}{4 (d+e x)^2 \left (e (a e-b d)+c d^2\right )}\right )+\frac {2 (a+x (b+c x))^{3/2} (2 a e-b d+b e x-2 c d x)}{(d+e x)^4}\right )}{192 \left (e (a e-b d)+c d^2\right )^3}-\frac {7 e (a+x (b+c x))^{5/2} (2 c d-b e)}{60 (d+e x)^5 \left (e (a e-b d)+c d^2\right )^2}-\frac {e (a+x (b+c x))^{5/2}}{6 (d+e x)^6 \left (e (a e-b d)+c d^2\right )} \end {gather*}

Antiderivative was successfully verified.

[In]

Integrate[(a + b*x + c*x^2)^(3/2)/(d + e*x)^7,x]

[Out]

-1/6*(e*(a + x*(b + c*x))^(5/2))/((c*d^2 + e*(-(b*d) + a*e))*(d + e*x)^6) - (7*e*(2*c*d - b*e)*(a + x*(b + c*x
))^(5/2))/(60*(c*d^2 + e*(-(b*d) + a*e))^2*(d + e*x)^5) - ((12*c^2*d^2 + (7*b^2*e^2)/2 - 2*c*e*(6*b*d + a*e))*
((2*(-(b*d) + 2*a*e - 2*c*d*x + b*e*x)*(a + x*(b + c*x))^(3/2))/(d + e*x)^4 + 3*(b^2 - 4*a*c)*((Sqrt[a + x*(b
+ c*x)]*(-2*a*e + 2*c*d*x + b*(d - e*x)))/(4*(c*d^2 + e*(-(b*d) + a*e))*(d + e*x)^2) + ((b^2 - 4*a*c)*ArcTanh[
(-(b*d) + 2*a*e - 2*c*d*x + b*e*x)/(2*Sqrt[c*d^2 + e*(-(b*d) + a*e)]*Sqrt[a + x*(b + c*x)])])/(8*(c*d^2 + e*(-
(b*d) + a*e))^(3/2)))))/(192*(c*d^2 + e*(-(b*d) + a*e))^3)

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IntegrateAlgebraic [F]  time = 180.01, size = 0, normalized size = 0.00 \begin {gather*} \text {\$Aborted} \end {gather*}

Verification is not applicable to the result.

[In]

IntegrateAlgebraic[(a + b*x + c*x^2)^(3/2)/(d + e*x)^7,x]

[Out]

$Aborted

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fricas [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((c*x^2+b*x+a)^(3/2)/(e*x+d)^7,x, algorithm="fricas")

[Out]

Timed out

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giac [B]  time = 73.47, size = 14083, normalized size = 34.43

result too large to display

Verification of antiderivative is not currently implemented for this CAS.

[In]

integrate((c*x^2+b*x+a)^(3/2)/(e*x+d)^7,x, algorithm="giac")

[Out]

1/512*(24*b^4*c^2*d^2 - 192*a*b^2*c^3*d^2 + 384*a^2*c^4*d^2 - 24*b^5*c*d*e + 192*a*b^3*c^2*d*e - 384*a^2*b*c^3
*d*e + 7*b^6*e^2 - 60*a*b^4*c*e^2 + 144*a^2*b^2*c^2*e^2 - 64*a^3*c^3*e^2)*arctan(-((sqrt(c)*x - sqrt(c*x^2 + b
*x + a))*e + sqrt(c)*d)/sqrt(-c*d^2 + b*d*e - a*e^2))/((c^4*d^8 - 4*b*c^3*d^7*e + 6*b^2*c^2*d^6*e^2 + 4*a*c^3*
d^6*e^2 - 4*b^3*c*d^5*e^3 - 12*a*b*c^2*d^5*e^3 + b^4*d^4*e^4 + 12*a*b^2*c*d^4*e^4 + 6*a^2*c^2*d^4*e^4 - 4*a*b^
3*d^3*e^5 - 12*a^2*b*c*d^3*e^5 + 6*a^2*b^2*d^2*e^6 + 4*a^3*c*d^2*e^6 - 4*a^3*b*d*e^7 + a^4*e^8)*sqrt(-c*d^2 +
b*d*e - a*e^2)) + 1/7680*(24576*(sqrt(c)*x - sqrt(c*x^2 + b*x + a))^7*c^8*d^10*e + 8192*(sqrt(c)*x - sqrt(c*x^
2 + b*x + a))^6*c^(17/2)*d^11 + 30720*(sqrt(c)*x - sqrt(c*x^2 + b*x + a))^8*c^(15/2)*d^9*e^2 + 40960*(sqrt(c)*
x - sqrt(c*x^2 + b*x + a))^6*b*c^(15/2)*d^10*e + 24576*(sqrt(c)*x - sqrt(c*x^2 + b*x + a))^5*b*c^8*d^11 + 2048
0*(sqrt(c)*x - sqrt(c*x^2 + b*x + a))^9*c^7*d^8*e^3 - 24576*(sqrt(c)*x - sqrt(c*x^2 + b*x + a))^5*a*c^8*d^10*e
+ 30720*(sqrt(c)*x - sqrt(c*x^2 + b*x + a))^4*b^2*c^(15/2)*d^11 - 46080*(sqrt(c)*x - sqrt(c*x^2 + b*x + a))^8
*b*c^(13/2)*d^8*e^3 - 101376*(sqrt(c)*x - sqrt(c*x^2 + b*x + a))^6*b^2*c^(13/2)*d^9*e^2 - 4096*(sqrt(c)*x - sq
rt(c*x^2 + b*x + a))^6*a*c^(15/2)*d^9*e^2 - 46080*(sqrt(c)*x - sqrt(c*x^2 + b*x + a))^4*b^3*c^(13/2)*d^10*e -
61440*(sqrt(c)*x - sqrt(c*x^2 + b*x + a))^4*a*b*c^(15/2)*d^10*e + 20480*(sqrt(c)*x - sqrt(c*x^2 + b*x + a))^3*
b^3*c^7*d^11 - 81920*(sqrt(c)*x - sqrt(c*x^2 + b*x + a))^9*b*c^6*d^7*e^4 - 119808*(sqrt(c)*x - sqrt(c*x^2 + b*
x + a))^7*b^2*c^6*d^8*e^3 + 110592*(sqrt(c)*x - sqrt(c*x^2 + b*x + a))^7*a*c^7*d^8*e^3 - 119808*(sqrt(c)*x - s
qrt(c*x^2 + b*x + a))^5*b^3*c^6*d^9*e^2 + 110592*(sqrt(c)*x - sqrt(c*x^2 + b*x + a))^5*a*b*c^7*d^9*e^2 - 43520
*(sqrt(c)*x - sqrt(c*x^2 + b*x + a))^3*b^4*c^6*d^10*e - 61440*(sqrt(c)*x - sqrt(c*x^2 + b*x + a))^3*a*b^2*c^7*
d^10*e + 7680*(sqrt(c)*x - sqrt(c*x^2 + b*x + a))^2*b^4*c^(13/2)*d^11 - 122880*(sqrt(c)*x - sqrt(c*x^2 + b*x +
a))^8*b^2*c^(11/2)*d^7*e^4 + 122880*(sqrt(c)*x - sqrt(c*x^2 + b*x + a))^8*a*c^(13/2)*d^7*e^4 - 55296*(sqrt(c)
*x - sqrt(c*x^2 + b*x + a))^6*b^3*c^(11/2)*d^8*e^3 + 405504*(sqrt(c)*x - sqrt(c*x^2 + b*x + a))^6*a*b*c^(13/2)
*d^8*e^3 - 51840*(sqrt(c)*x - sqrt(c*x^2 + b*x + a))^4*b^4*c^(11/2)*d^9*e^2 + 276480*(sqrt(c)*x - sqrt(c*x^2 +
b*x + a))^4*a*b^2*c^(13/2)*d^9*e^2 + 30720*(sqrt(c)*x - sqrt(c*x^2 + b*x + a))^4*a^2*c^(15/2)*d^9*e^2 - 18432
*(sqrt(c)*x - sqrt(c*x^2 + b*x + a))^2*b^5*c^(11/2)*d^10*e - 30720*(sqrt(c)*x - sqrt(c*x^2 + b*x + a))^2*a*b^3
*c^(13/2)*d^10*e + 1536*(sqrt(c)*x - sqrt(c*x^2 + b*x + a))*b^5*c^6*d^11 + 122880*(sqrt(c)*x - sqrt(c*x^2 + b*
x + a))^9*b^2*c^5*d^6*e^5 + 81920*(sqrt(c)*x - sqrt(c*x^2 + b*x + a))^9*a*c^6*d^6*e^5 - 12288*(sqrt(c)*x - sqr
t(c*x^2 + b*x + a))^7*b^3*c^5*d^7*e^4 + 49152*(sqrt(c)*x - sqrt(c*x^2 + b*x + a))^7*a*b*c^6*d^7*e^4 + 41472*(s
qrt(c)*x - sqrt(c*x^2 + b*x + a))^5*b^4*c^5*d^8*e^3 + 414720*(sqrt(c)*x - sqrt(c*x^2 + b*x + a))^5*a*b^2*c^6*d
^8*e^3 - 110592*(sqrt(c)*x - sqrt(c*x^2 + b*x + a))^5*a^2*c^7*d^8*e^3 - 3840*(sqrt(c)*x - sqrt(c*x^2 + b*x + a
))^3*b^5*c^5*d^9*e^2 + 266240*(sqrt(c)*x - sqrt(c*x^2 + b*x + a))^3*a*b^3*c^6*d^9*e^2 + 61440*(sqrt(c)*x - sqr
t(c*x^2 + b*x + a))^3*a^2*b*c^7*d^9*e^2 - 3840*(sqrt(c)*x - sqrt(c*x^2 + b*x + a))*b^6*c^5*d^10*e - 7680*(sqrt
(c)*x - sqrt(c*x^2 + b*x + a))*a*b^4*c^6*d^10*e + 128*b^6*c^(11/2)*d^11 + 337920*(sqrt(c)*x - sqrt(c*x^2 + b*x
+ a))^8*b^3*c^(9/2)*d^6*e^5 - 61440*(sqrt(c)*x - sqrt(c*x^2 + b*x + a))^8*a*b*c^(11/2)*d^6*e^5 + 100800*(sqrt
(c)*x - sqrt(c*x^2 + b*x + a))^6*b^4*c^(9/2)*d^7*e^4 - 450048*(sqrt(c)*x - sqrt(c*x^2 + b*x + a))^6*a*b^2*c^(1
1/2)*d^7*e^4 - 549888*(sqrt(c)*x - sqrt(c*x^2 + b*x + a))^6*a^2*c^(13/2)*d^7*e^4 + 60480*(sqrt(c)*x - sqrt(c*x
^2 + b*x + a))^4*b^5*c^(9/2)*d^8*e^3 + 69120*(sqrt(c)*x - sqrt(c*x^2 + b*x + a))^4*a*b^3*c^(11/2)*d^8*e^3 - 41
4720*(sqrt(c)*x - sqrt(c*x^2 + b*x + a))^4*a^2*b*c^(13/2)*d^8*e^3 + 3840*(sqrt(c)*x - sqrt(c*x^2 + b*x + a))^2
*b^6*c^(9/2)*d^9*e^2 + 126720*(sqrt(c)*x - sqrt(c*x^2 + b*x + a))^2*a*b^4*c^(11/2)*d^9*e^2 + 46080*(sqrt(c)*x
- sqrt(c*x^2 + b*x + a))^2*a^2*b^2*c^(13/2)*d^9*e^2 - 320*b^7*c^(9/2)*d^10*e - 768*a*b^5*c^(11/2)*d^10*e - 819
20*(sqrt(c)*x - sqrt(c*x^2 + b*x + a))^9*b^3*c^4*d^5*e^6 - 245760*(sqrt(c)*x - sqrt(c*x^2 + b*x + a))^9*a*b*c^
5*d^5*e^6 + 336960*(sqrt(c)*x - sqrt(c*x^2 + b*x + a))^7*b^4*c^4*d^6*e^5 + 93696*(sqrt(c)*x - sqrt(c*x^2 + b*x
+ a))^7*a*b^2*c^5*d^6*e^5 - 605184*(sqrt(c)*x - sqrt(c*x^2 + b*x + a))^7*a^2*c^6*d^6*e^5 + 87360*(sqrt(c)*x -
sqrt(c*x^2 + b*x + a))^5*b^5*c^4*d^7*e^4 - 600576*(sqrt(c)*x - sqrt(c*x^2 + b*x + a))^5*a*b^3*c^5*d^7*e^4 - 1
207296*(sqrt(c)*x - sqrt(c*x^2 + b*x + a))^5*a^2*b*c^6*d^7*e^4 + 33920*(sqrt(c)*x - sqrt(c*x^2 + b*x + a))^3*b
^6*c^4*d^8*e^3 - 130560*(sqrt(c)*x - sqrt(c*x^2 + b*x + a))^3*a*b^4*c^5*d^8*e^3 - 537600*(sqrt(c)*x - sqrt(c*x
^2 + b*x + a))^3*a^2*b^2*c^6*d^8*e^3 - 20480*(sqrt(c)*x - sqrt(c*x^2 + b*x + a))^3*a^3*c^7*d^8*e^3 + 1152*(sqr
t(c)*x - sqrt(c*x^2 + b*x + a))*b^7*c^4*d^9*e^2 + 29952*(sqrt(c)*x - sqrt(c*x^2 + b*x + a))*a*b^5*c^5*d^9*e^2
+ 15360*(sqrt(c)*x - sqrt(c*x^2 + b*x + a))*a^2*b^3*c^6*d^9*e^2 - 317520*(sqrt(c)*x - sqrt(c*x^2 + b*x + a))^8
*b^4*c^(7/2)*d^5*e^6 - 224640*(sqrt(c)*x - sqrt(c*x^2 + b*x + a))^8*a*b^2*c^(9/2)*d^5*e^6 - 472320*(sqrt(c)*x
- sqrt(c*x^2 + b*x + a))^8*a^2*c^(11/2)*d^5*e^6 + 95424*(sqrt(c)*x - sqrt(c*x^2 + b*x + a))^6*b^5*c^(7/2)*d^6*
e^5 + 698880*(sqrt(c)*x - sqrt(c*x^2 + b*x + a))^6*a*b^3*c^(9/2)*d^6*e^5 - 193536*(sqrt(c)*x - sqrt(c*x^2 + b*
x + a))^6*a^2*b*c^(11/2)*d^6*e^5 + 15120*(sqrt(c)*x - sqrt(c*x^2 + b*x + a))^4*b^6*c^(7/2)*d^7*e^4 - 228480*(s
qrt(c)*x - sqrt(c*x^2 + b*x + a))^4*a*b^4*c^(9/2)*d^7*e^4 - 864000*(sqrt(c)*x - sqrt(c*x^2 + b*x + a))^4*a^2*b
^2*c^(11/2)*d^7*e^4 + 245760*(sqrt(c)*x - sqrt(c*x^2 + b*x + a))^4*a^3*c^(13/2)*d^7*e^4 + 11136*(sqrt(c)*x - s
qrt(c*x^2 + b*x + a))^2*b^7*c^(7/2)*d^8*e^3 - 88704*(sqrt(c)*x - sqrt(c*x^2 + b*x + a))^2*a*b^5*c^(9/2)*d^8*e^
3 - 322560*(sqrt(c)*x - sqrt(c*x^2 + b*x + a))^2*a^2*b^3*c^(11/2)*d^8*e^3 - 30720*(sqrt(c)*x - sqrt(c*x^2 + b*
x + a))^2*a^3*b*c^(13/2)*d^8*e^3 + 96*b^8*c^(7/2)*d^9*e^2 + 2816*a*b^6*c^(9/2)*d^9*e^2 + 1920*a^2*b^4*c^(11/2)
*d^9*e^2 + 2720*(sqrt(c)*x - sqrt(c*x^2 + b*x + a))^9*b^4*c^3*d^4*e^7 + 387840*(sqrt(c)*x - sqrt(c*x^2 + b*x +
a))^9*a*b^2*c^4*d^4*e^7 - 161280*(sqrt(c)*x - sqrt(c*x^2 + b*x + a))^9*a^2*c^5*d^4*e^7 - 419328*(sqrt(c)*x -
sqrt(c*x^2 + b*x + a))^7*b^5*c^3*d^5*e^6 - 368640*(sqrt(c)*x - sqrt(c*x^2 + b*x + a))^7*a*b^3*c^4*d^5*e^6 - 73
728*(sqrt(c)*x - sqrt(c*x^2 + b*x + a))^7*a^2*b*c^5*d^5*e^6 - 71808*(sqrt(c)*x - sqrt(c*x^2 + b*x + a))^5*b^6*
c^3*d^6*e^5 + 822720*(sqrt(c)*x - sqrt(c*x^2 + b*x + a))^5*a*b^4*c^4*d^6*e^5 + 907776*(sqrt(c)*x - sqrt(c*x^2
+ b*x + a))^5*a^2*b^2*c^5*d^6*e^5 + 1219584*(sqrt(c)*x - sqrt(c*x^2 + b*x + a))^5*a^3*c^6*d^6*e^5 - 18080*(sqr
t(c)*x - sqrt(c*x^2 + b*x + a))^3*b^7*c^3*d^7*e^4 + 42240*(sqrt(c)*x - sqrt(c*x^2 + b*x + a))^3*a*b^5*c^4*d^7*
e^4 - 145920*(sqrt(c)*x - sqrt(c*x^2 + b*x + a))^3*a^2*b^3*c^5*d^7*e^4 + 573440*(sqrt(c)*x - sqrt(c*x^2 + b*x
+ a))^3*a^3*b*c^6*d^7*e^4 + 2112*(sqrt(c)*x - sqrt(c*x^2 + b*x + a))*b^8*c^3*d^8*e^3 - 21888*(sqrt(c)*x - sqrt
(c*x^2 + b*x + a))*a*b^6*c^4*d^8*e^3 - 92160*(sqrt(c)*x - sqrt(c*x^2 + b*x + a))*a^2*b^4*c^5*d^8*e^3 - 15360*(
sqrt(c)*x - sqrt(c*x^2 + b*x + a))*a^3*b^2*c^6*d^8*e^3 - 3960*(sqrt(c)*x - sqrt(c*x^2 + b*x + a))^10*b^4*c^(5/
2)*d^3*e^8 + 31680*(sqrt(c)*x - sqrt(c*x^2 + b*x + a))^10*a*b^2*c^(7/2)*d^3*e^8 - 63360*(sqrt(c)*x - sqrt(c*x^
2 + b*x + a))^10*a^2*c^(9/2)*d^3*e^8 + 99480*(sqrt(c)*x - sqrt(c*x^2 + b*x + a))^8*b^5*c^(5/2)*d^4*e^7 + 61728
0*(sqrt(c)*x - sqrt(c*x^2 + b*x + a))^8*a*b^3*c^(7/2)*d^4*e^7 + 455040*(sqrt(c)*x - sqrt(c*x^2 + b*x + a))^8*a
^2*b*c^(9/2)*d^4*e^7 - 242840*(sqrt(c)*x - sqrt(c*x^2 + b*x + a))^6*b^6*c^(5/2)*d^5*e^6 - 593760*(sqrt(c)*x -
sqrt(c*x^2 + b*x + a))^6*a*b^4*c^(7/2)*d^5*e^6 - 1011840*(sqrt(c)*x - sqrt(c*x^2 + b*x + a))^6*a^2*b^2*c^(9/2)
*d^5*e^6 + 1564160*(sqrt(c)*x - sqrt(c*x^2 + b*x + a))^6*a^3*c^(11/2)*d^5*e^6 - 64440*(sqrt(c)*x - sqrt(c*x^2
+ b*x + a))^4*b^7*c^(5/2)*d^6*e^5 + 437280*(sqrt(c)*x - sqrt(c*x^2 + b*x + a))^4*a*b^5*c^(7/2)*d^6*e^5 + 67008
0*(sqrt(c)*x - sqrt(c*x^2 + b*x + a))^4*a^2*b^3*c^(9/2)*d^6*e^5 + 2188800*(sqrt(c)*x - sqrt(c*x^2 + b*x + a))^
4*a^3*b*c^(11/2)*d^6*e^5 - 12384*(sqrt(c)*x - sqrt(c*x^2 + b*x + a))^2*b^8*c^(5/2)*d^7*e^4 + 54816*(sqrt(c)*x
- sqrt(c*x^2 + b*x + a))^2*a*b^6*c^(7/2)*d^7*e^4 + 89280*(sqrt(c)*x - sqrt(c*x^2 + b*x + a))^2*a^2*b^4*c^(9/2)
*d^7*e^4 + 476160*(sqrt(c)*x - sqrt(c*x^2 + b*x + a))^2*a^3*b^2*c^(11/2)*d^7*e^4 + 15360*(sqrt(c)*x - sqrt(c*x
^2 + b*x + a))^2*a^4*c^(13/2)*d^7*e^4 + 176*b^9*c^(5/2)*d^8*e^3 - 1920*a*b^7*c^(7/2)*d^8*e^3 - 10176*a^2*b^5*c
^(9/2)*d^8*e^3 - 2560*a^3*b^3*c^(11/2)*d^8*e^3 - 360*(sqrt(c)*x - sqrt(c*x^2 + b*x + a))^11*b^4*c^2*d^2*e^9 +
2880*(sqrt(c)*x - sqrt(c*x^2 + b*x + a))^11*a*b^2*c^3*d^2*e^9 - 5760*(sqrt(c)*x - sqrt(c*x^2 + b*x + a))^11*a^
2*c^4*d^2*e^9 + 15720*(sqrt(c)*x - sqrt(c*x^2 + b*x + a))^9*b^5*c^2*d^3*e^8 - 207680*(sqrt(c)*x - sqrt(c*x^2 +
b*x + a))^9*a*b^3*c^3*d^3*e^8 + 5760*(sqrt(c)*x - sqrt(c*x^2 + b*x + a))^9*a^2*b*c^4*d^3*e^8 + 170520*(sqrt(c
)*x - sqrt(c*x^2 + b*x + a))^7*b^6*c^2*d^4*e^7 + 846240*(sqrt(c)*x - sqrt(c*x^2 + b*x + a))^7*a*b^4*c^3*d^4*e^
7 + 5760*(sqrt(c)*x - sqrt(c*x^2 + b*x + a))^7*a^2*b^2*c^4*d^4*e^7 + 1328640*(sqrt(c)*x - sqrt(c*x^2 + b*x + a
))^7*a^3*c^5*d^4*e^7 - 47400*(sqrt(c)*x - sqrt(c*x^2 + b*x + a))^5*b^7*c^2*d^5*e^6 - 362592*(sqrt(c)*x - sqrt(
c*x^2 + b*x + a))^5*a*b^5*c^3*d^5*e^6 - 2436480*(sqrt(c)*x - sqrt(c*x^2 + b*x + a))^5*a^2*b^3*c^4*d^5*e^6 + 10
33728*(sqrt(c)*x - sqrt(c*x^2 + b*x + a))^5*a^3*b*c^5*d^5*e^6 - 16320*(sqrt(c)*x - sqrt(c*x^2 + b*x + a))^3*b^
8*c^2*d^6*e^5 + 129920*(sqrt(c)*x - sqrt(c*x^2 + b*x + a))^3*a*b^6*c^3*d^6*e^5 - 52800*(sqrt(c)*x - sqrt(c*x^2
+ b*x + a))^3*a^2*b^4*c^4*d^6*e^5 + 1374720*(sqrt(c)*x - sqrt(c*x^2 + b*x + a))^3*a^3*b^2*c^5*d^6*e^5 - 18944
0*(sqrt(c)*x - sqrt(c*x^2 + b*x + a))^3*a^4*c^6*d^6*e^5 - 3120*(sqrt(c)*x - sqrt(c*x^2 + b*x + a))*b^9*c^2*d^7
*e^4 + 14496*(sqrt(c)*x - sqrt(c*x^2 + b*x + a))*a*b^7*c^3*d^7*e^4 + 40896*(sqrt(c)*x - sqrt(c*x^2 + b*x + a))
*a^2*b^5*c^4*d^7*e^4 + 168960*(sqrt(c)*x - sqrt(c*x^2 + b*x + a))*a^3*b^3*c^5*d^7*e^4 + 15360*(sqrt(c)*x - sqr
t(c*x^2 + b*x + a))*a^4*b*c^6*d^7*e^4 + 3960*(sqrt(c)*x - sqrt(c*x^2 + b*x + a))^10*b^5*c^(3/2)*d^2*e^9 - 3168
0*(sqrt(c)*x - sqrt(c*x^2 + b*x + a))^10*a*b^3*c^(5/2)*d^2*e^9 + 63360*(sqrt(c)*x - sqrt(c*x^2 + b*x + a))^10*
a^2*b*c^(7/2)*d^2*e^9 + 6390*(sqrt(c)*x - sqrt(c*x^2 + b*x + a))^8*b^6*c^(3/2)*d^3*e^8 - 333120*(sqrt(c)*x - s
qrt(c*x^2 + b*x + a))^8*a*b^4*c^(5/2)*d^3*e^8 - 836640*(sqrt(c)*x - sqrt(c*x^2 + b*x + a))^8*a^2*b^2*c^(7/2)*d
^3*e^8 + 526080*(sqrt(c)*x - sqrt(c*x^2 + b*x + a))^8*a^3*c^(9/2)*d^3*e^8 + 115328*(sqrt(c)*x - sqrt(c*x^2 + b
*x + a))^6*b^7*c^(3/2)*d^4*e^7 + 793248*(sqrt(c)*x - sqrt(c*x^2 + b*x + a))^6*a*b^5*c^(5/2)*d^4*e^7 + 480000*(
sqrt(c)*x - sqrt(c*x^2 + b*x + a))^6*a^2*b^3*c^(7/2)*d^4*e^7 + 739840*(sqrt(c)*x - sqrt(c*x^2 + b*x + a))^6*a^
3*b*c^(9/2)*d^4*e^7 + 14460*(sqrt(c)*x - sqrt(c*x^2 + b*x + a))^4*b^8*c^(3/2)*d^5*e^6 - 81720*(sqrt(c)*x - sqr
t(c*x^2 + b*x + a))^4*a*b^6*c^(5/2)*d^5*e^6 - 1728000*(sqrt(c)*x - sqrt(c*x^2 + b*x + a))^4*a^2*b^4*c^(7/2)*d^
5*e^6 - 792960*(sqrt(c)*x - sqrt(c*x^2 + b*x + a))^4*a^3*b^2*c^(9/2)*d^5*e^6 - 1198080*(sqrt(c)*x - sqrt(c*x^2
+ b*x + a))^4*a^4*c^(11/2)*d^5*e^6 + 600*(sqrt(c)*x - sqrt(c*x^2 + b*x + a))^2*b^9*c^(3/2)*d^6*e^5 + 26928*(s
qrt(c)*x - sqrt(c*x^2 + b*x + a))^2*a*b^7*c^(5/2)*d^6*e^5 - 185472*(sqrt(c)*x - sqrt(c*x^2 + b*x + a))^2*a^2*b
^5*c^(7/2)*d^6*e^5 + 357120*(sqrt(c)*x - sqrt(c*x^2 + b*x + a))^2*a^3*b^3*c^(9/2)*d^6*e^5 - 337920*(sqrt(c)*x
- sqrt(c*x^2 + b*x + a))^2*a^4*b*c^(11/2)*d^6*e^5 - 290*b^10*c^(3/2)*d^7*e^4 + 1272*a*b^8*c^(5/2)*d^7*e^4 + 47
52*a^2*b^6*c^(7/2)*d^7*e^4 + 21760*a^3*b^4*c^(9/2)*d^7*e^4 + 3840*a^4*b^2*c^(11/2)*d^7*e^4 + 360*(sqrt(c)*x -
sqrt(c*x^2 + b*x + a))^11*b^5*c*d*e^10 - 2880*(sqrt(c)*x - sqrt(c*x^2 + b*x + a))^11*a*b^3*c^2*d*e^10 + 5760*(
sqrt(c)*x - sqrt(c*x^2 + b*x + a))^11*a^2*b*c^3*d*e^10 - 3140*(sqrt(c)*x - sqrt(c*x^2 + b*x + a))^9*b^6*c*d^2*
e^9 + 30120*(sqrt(c)*x - sqrt(c*x^2 + b*x + a))^9*a*b^4*c^2*d^2*e^9 + 32640*(sqrt(c)*x - sqrt(c*x^2 + b*x + a)
)^9*a^2*b^2*c^3*d^2*e^9 + 161920*(sqrt(c)*x - sqrt(c*x^2 + b*x + a))^9*a^3*c^4*d^2*e^9 - 13896*(sqrt(c)*x - sq
rt(c*x^2 + b*x + a))^7*b^7*c*d^3*e^8 - 436416*(sqrt(c)*x - sqrt(c*x^2 + b*x + a))^7*a*b^5*c^2*d^3*e^8 - 842880
*(sqrt(c)*x - sqrt(c*x^2 + b*x + a))^7*a^2*b^3*c^3*d^3*e^8 - 552960*(sqrt(c)*x - sqrt(c*x^2 + b*x + a))^7*a^3*
b*c^4*d^3*e^8 + 38784*(sqrt(c)*x - sqrt(c*x^2 + b*x + a))^5*b^8*c*d^4*e^7 + 308424*(sqrt(c)*x - sqrt(c*x^2 + b
*x + a))^5*a*b^6*c^2*d^4*e^7 + 1435680*(sqrt(c)*x - sqrt(c*x^2 + b*x + a))^5*a^2*b^4*c^3*d^4*e^7 + 1192320*(sq
rt(c)*x - sqrt(c*x^2 + b*x + a))^5*a^3*b^2*c^4*d^4*e^7 - 1374720*(sqrt(c)*x - sqrt(c*x^2 + b*x + a))^5*a^4*c^5
*d^4*e^7 + 9440*(sqrt(c)*x - sqrt(c*x^2 + b*x + a))^3*b^9*c*d^5*e^6 - 14160*(sqrt(c)*x - sqrt(c*x^2 + b*x + a)
)^3*a*b^7*c^2*d^5*e^6 - 454080*(sqrt(c)*x - sqrt(c*x^2 + b*x + a))^3*a^2*b^5*c^3*d^5*e^6 - 684800*(sqrt(c)*x -
sqrt(c*x^2 + b*x + a))^3*a^3*b^3*c^4*d^5*e^6 - 1827840*(sqrt(c)*x - sqrt(c*x^2 + b*x + a))^3*a^4*b*c^5*d^5*e^
6 + 900*(sqrt(c)*x - sqrt(c*x^2 + b*x + a))*b^10*c*d^6*e^5 + 5040*(sqrt(c)*x - sqrt(c*x^2 + b*x + a))*a*b^8*c^
2*d^6*e^5 - 64128*(sqrt(c)*x - sqrt(c*x^2 + b*x + a))*a^2*b^6*c^3*d^6*e^5 + 37440*(sqrt(c)*x - sqrt(c*x^2 + b*
x + a))*a^3*b^4*c^4*d^6*e^5 - 192000*(sqrt(c)*x - sqrt(c*x^2 + b*x + a))*a^4*b^2*c^5*d^6*e^5 - 3072*(sqrt(c)*x
- sqrt(c*x^2 + b*x + a))*a^5*c^6*d^6*e^5 - 1155*(sqrt(c)*x - sqrt(c*x^2 + b*x + a))^10*b^6*sqrt(c)*d*e^10 + 9
900*(sqrt(c)*x - sqrt(c*x^2 + b*x + a))^10*a*b^4*c^(3/2)*d*e^10 - 23760*(sqrt(c)*x - sqrt(c*x^2 + b*x + a))^10
*a^2*b^2*c^(5/2)*d*e^10 + 10560*(sqrt(c)*x - sqrt(c*x^2 + b*x + a))^10*a^3*c^(7/2)*d*e^10 - 5355*(sqrt(c)*x -
sqrt(c*x^2 + b*x + a))^8*b^7*sqrt(c)*d^2*e^9 + 27540*(sqrt(c)*x - sqrt(c*x^2 + b*x + a))^8*a*b^5*c^(3/2)*d^2*e
^9 + 497520*(sqrt(c)*x - sqrt(c*x^2 + b*x + a))^8*a^2*b^3*c^(5/2)*d^2*e^9 - 60480*(sqrt(c)*x - sqrt(c*x^2 + b*
x + a))^8*a^3*b*c^(7/2)*d^2*e^9 - 9702*(sqrt(c)*x - sqrt(c*x^2 + b*x + a))^6*b^8*sqrt(c)*d^3*e^8 - 403352*(sqr
t(c)*x - sqrt(c*x^2 + b*x + a))^6*a*b^6*c^(3/2)*d^3*e^8 - 693840*(sqrt(c)*x - sqrt(c*x^2 + b*x + a))^6*a^2*b^4
*c^(5/2)*d^3*e^8 - 756480*(sqrt(c)*x - sqrt(c*x^2 + b*x + a))^6*a^3*b^2*c^(7/2)*d^3*e^8 - 951040*(sqrt(c)*x -
sqrt(c*x^2 + b*x + a))^6*a^4*c^(9/2)*d^3*e^8 + 6930*(sqrt(c)*x - sqrt(c*x^2 + b*x + a))^4*b^9*sqrt(c)*d^4*e^7
- 3120*(sqrt(c)*x - sqrt(c*x^2 + b*x + a))^4*a*b^7*c^(3/2)*d^4*e^7 + 997200*(sqrt(c)*x - sqrt(c*x^2 + b*x + a)
)^4*a^2*b^5*c^(5/2)*d^4*e^7 + 1948800*(sqrt(c)*x - sqrt(c*x^2 + b*x + a))^4*a^3*b^3*c^(7/2)*d^4*e^7 - 441600*(
sqrt(c)*x - sqrt(c*x^2 + b*x + a))^4*a^4*b*c^(9/2)*d^4*e^7 + 1785*(sqrt(c)*x - sqrt(c*x^2 + b*x + a))^2*b^10*s
qrt(c)*d^5*e^6 - 10980*(sqrt(c)*x - sqrt(c*x^2 + b*x + a))^2*a*b^8*c^(3/2)*d^5*e^6 - 14184*(sqrt(c)*x - sqrt(c
*x^2 + b*x + a))^2*a^2*b^6*c^(5/2)*d^5*e^6 - 26400*(sqrt(c)*x - sqrt(c*x^2 + b*x + a))^2*a^3*b^4*c^(7/2)*d^5*e
^6 - 996480*(sqrt(c)*x - sqrt(c*x^2 + b*x + a))^2*a^4*b^2*c^(9/2)*d^5*e^6 + 105984*(sqrt(c)*x - sqrt(c*x^2 + b
*x + a))^2*a^5*c^(11/2)*d^5*e^6 + 105*b^11*sqrt(c)*d^6*e^5 + 620*a*b^9*c^(3/2)*d^6*e^5 - 7512*a^2*b^7*c^(5/2)*
d^6*e^5 + 2592*a^3*b^5*c^(7/2)*d^6*e^5 - 35200*a^4*b^3*c^(9/2)*d^6*e^5 - 1536*a^5*b*c^(11/2)*d^6*e^5 - 105*(sq
rt(c)*x - sqrt(c*x^2 + b*x + a))^11*b^6*e^11 + 900*(sqrt(c)*x - sqrt(c*x^2 + b*x + a))^11*a*b^4*c*e^11 - 2160*
(sqrt(c)*x - sqrt(c*x^2 + b*x + a))^11*a^2*b^2*c^2*e^11 + 960*(sqrt(c)*x - sqrt(c*x^2 + b*x + a))^11*a^3*c^3*e
^11 - 595*(sqrt(c)*x - sqrt(c*x^2 + b*x + a))^9*b^7*d*e^10 + 3060*(sqrt(c)*x - sqrt(c*x^2 + b*x + a))^9*a*b^5*
c*d*e^10 + 4080*(sqrt(c)*x - sqrt(c*x^2 + b*x + a))^9*a^2*b^3*c^2*d*e^10 - 109120*(sqrt(c)*x - sqrt(c*x^2 + b*
x + a))^9*a^3*b*c^3*d*e^10 - 1386*(sqrt(c)*x - sqrt(c*x^2 + b*x + a))^7*b^8*d^2*e^9 + 21024*(sqrt(c)*x - sqrt(
c*x^2 + b*x + a))^7*a*b^6*c*d^2*e^9 + 638640*(sqrt(c)*x - sqrt(c*x^2 + b*x + a))^7*a^2*b^4*c^2*d^2*e^9 + 46656
0*(sqrt(c)*x - sqrt(c*x^2 + b*x + a))^7*a^3*b^2*c^3*d^2*e^9 - 172800*(sqrt(c)*x - sqrt(c*x^2 + b*x + a))^7*a^4
*c^4*d^2*e^9 - 1686*(sqrt(c)*x - sqrt(c*x^2 + b*x + a))^5*b^9*d^3*e^8 - 183000*(sqrt(c)*x - sqrt(c*x^2 + b*x +
a))^5*a*b^7*c*d^3*e^8 - 545904*(sqrt(c)*x - sqrt(c*x^2 + b*x + a))^5*a^2*b^5*c^2*d^3*e^8 - 1482240*(sqrt(c)*x
- sqrt(c*x^2 + b*x + a))^5*a^3*b^3*c^3*d^3*e^8 - 103680*(sqrt(c)*x - sqrt(c*x^2 + b*x + a))^5*a^4*b*c^4*d^3*e
^8 + 595*(sqrt(c)*x - sqrt(c*x^2 + b*x + a))^3*b^10*d^4*e^7 - 31380*(sqrt(c)*x - sqrt(c*x^2 + b*x + a))^3*a*b^
8*c*d^4*e^7 + 280200*(sqrt(c)*x - sqrt(c*x^2 + b*x + a))^3*a^2*b^6*c^2*d^4*e^7 + 965600*(sqrt(c)*x - sqrt(c*x^
2 + b*x + a))^3*a^3*b^4*c^3*d^4*e^7 + 873600*(sqrt(c)*x - sqrt(c*x^2 + b*x + a))^3*a^4*b^2*c^4*d^4*e^7 + 77568
0*(sqrt(c)*x - sqrt(c*x^2 + b*x + a))^3*a^5*c^5*d^4*e^7 + 105*(sqrt(c)*x - sqrt(c*x^2 + b*x + a))*b^11*d^5*e^6
- 4140*(sqrt(c)*x - sqrt(c*x^2 + b*x + a))*a*b^9*c*d^5*e^6 + 11160*(sqrt(c)*x - sqrt(c*x^2 + b*x + a))*a^2*b^
7*c^2*d^5*e^6 + 66720*(sqrt(c)*x - sqrt(c*x^2 + b*x + a))*a^3*b^5*c^3*d^5*e^6 - 236160*(sqrt(c)*x - sqrt(c*x^2
+ b*x + a))*a^4*b^3*c^4*d^5*e^6 + 115200*(sqrt(c)*x - sqrt(c*x^2 + b*x + a))*a^5*b*c^5*d^5*e^6 + 5355*(sqrt(c
)*x - sqrt(c*x^2 + b*x + a))^8*a*b^6*sqrt(c)*d*e^10 - 45900*(sqrt(c)*x - sqrt(c*x^2 + b*x + a))^8*a^2*b^4*c^(3
/2)*d*e^10 - 197040*(sqrt(c)*x - sqrt(c*x^2 + b*x + a))^8*a^3*b^2*c^(5/2)*d*e^10 - 18240*(sqrt(c)*x - sqrt(c*x
^2 + b*x + a))^8*a^4*c^(7/2)*d*e^10 + 19404*(sqrt(c)*x - sqrt(c*x^2 + b*x + a))^6*a*b^7*sqrt(c)*d^2*e^9 + 5427
84*(sqrt(c)*x - sqrt(c*x^2 + b*x + a))^6*a^2*b^5*c^(3/2)*d^2*e^9 + 374720*(sqrt(c)*x - sqrt(c*x^2 + b*x + a))^
6*a^3*b^3*c^(5/2)*d^2*e^9 + 821760*(sqrt(c)*x - sqrt(c*x^2 + b*x + a))^6*a^4*b*c^(7/2)*d^2*e^9 - 36150*(sqrt(c
)*x - sqrt(c*x^2 + b*x + a))^4*a*b^8*sqrt(c)*d^3*e^8 - 162060*(sqrt(c)*x - sqrt(c*x^2 + b*x + a))^4*a^2*b^6*c^
(3/2)*d^3*e^8 - 1591200*(sqrt(c)*x - sqrt(c*x^2 + b*x + a))^4*a^3*b^4*c^(5/2)*d^3*e^8 - 619200*(sqrt(c)*x - sq
rt(c*x^2 + b*x + a))^4*a^4*b^2*c^(7/2)*d^3*e^8 + 744960*(sqrt(c)*x - sqrt(c*x^2 + b*x + a))^4*a^5*c^(9/2)*d^3*
e^8 - 7140*(sqrt(c)*x - sqrt(c*x^2 + b*x + a))^2*a*b^9*sqrt(c)*d^4*e^7 + 44640*(sqrt(c)*x - sqrt(c*x^2 + b*x +
a))^2*a^2*b^7*c^(3/2)*d^4*e^7 + 95520*(sqrt(c)*x - sqrt(c*x^2 + b*x + a))^2*a^3*b^5*c^(5/2)*d^4*e^7 + 518400*
(sqrt(c)*x - sqrt(c*x^2 + b*x + a))^2*a^4*b^3*c^(7/2)*d^4*e^7 + 898560*(sqrt(c)*x - sqrt(c*x^2 + b*x + a))^2*a
^5*b*c^(9/2)*d^4*e^7 - 525*a*b^10*sqrt(c)*d^5*e^6 + 1320*a^2*b^8*c^(3/2)*d^5*e^6 + 11704*a^3*b^6*c^(5/2)*d^5*e
^6 - 22320*a^4*b^4*c^(7/2)*d^5*e^6 + 30720*a^5*b^2*c^(9/2)*d^5*e^6 + 256*a^6*c^(11/2)*d^5*e^6 + 595*(sqrt(c)*x
- sqrt(c*x^2 + b*x + a))^9*a*b^6*e^11 - 5100*(sqrt(c)*x - sqrt(c*x^2 + b*x + a))^9*a^2*b^4*c*e^11 + 12240*(sq
rt(c)*x - sqrt(c*x^2 + b*x + a))^9*a^3*b^2*c^2*e^11 + 15040*(sqrt(c)*x - sqrt(c*x^2 + b*x + a))^9*a^4*c^3*e^11
+ 2772*(sqrt(c)*x - sqrt(c*x^2 + b*x + a))^7*a*b^7*d*e^10 - 19008*(sqrt(c)*x - sqrt(c*x^2 + b*x + a))^7*a^2*b
^5*c*d*e^10 - 484800*(sqrt(c)*x - sqrt(c*x^2 + b*x + a))^7*a^3*b^3*c^2*d*e^10 + 99840*(sqrt(c)*x - sqrt(c*x^2
+ b*x + a))^7*a^4*b*c^3*d*e^10 + 5058*(sqrt(c)*x - sqrt(c*x^2 + b*x + a))^5*a*b^8*d^2*e^9 + 292248*(sqrt(c)*x
- sqrt(c*x^2 + b*x + a))^5*a^2*b^6*c*d^2*e^9 + 462480*(sqrt(c)*x - sqrt(c*x^2 + b*x + a))^5*a^3*b^4*c^2*d^2*e^
9 + 748800*(sqrt(c)*x - sqrt(c*x^2 + b*x + a))^5*a^4*b^2*c^3*d^2*e^9 + 449280*(sqrt(c)*x - sqrt(c*x^2 + b*x +
a))^5*a^5*c^4*d^2*e^9 - 2380*(sqrt(c)*x - sqrt(c*x^2 + b*x + a))^3*a*b^9*d^3*e^8 + 11880*(sqrt(c)*x - sqrt(c*x
^2 + b*x + a))^3*a^2*b^7*c*d^3*e^8 - 645120*(sqrt(c)*x - sqrt(c*x^2 + b*x + a))^3*a^3*b^5*c^2*d^3*e^8 - 944000
*(sqrt(c)*x - sqrt(c*x^2 + b*x + a))^3*a^4*b^3*c^3*d^3*e^8 - 61440*(sqrt(c)*x - sqrt(c*x^2 + b*x + a))^3*a^5*b
*c^4*d^3*e^8 - 525*(sqrt(c)*x - sqrt(c*x^2 + b*x + a))*a*b^10*d^4*e^7 + 8460*(sqrt(c)*x - sqrt(c*x^2 + b*x + a
))*a^2*b^8*c*d^4*e^7 - 33960*(sqrt(c)*x - sqrt(c*x^2 + b*x + a))*a^3*b^6*c^2*d^4*e^7 + 66240*(sqrt(c)*x - sqrt
(c*x^2 + b*x + a))*a^4*b^4*c^3*d^4*e^7 + 337536*(sqrt(c)*x - sqrt(c*x^2 + b*x + a))*a^5*b^2*c^4*d^4*e^7 - 2150
4*(sqrt(c)*x - sqrt(c*x^2 + b*x + a))*a^6*c^5*d^4*e^7 + 76800*(sqrt(c)*x - sqrt(c*x^2 + b*x + a))^8*a^4*b*c^(5
/2)*e^11 - 9702*(sqrt(c)*x - sqrt(c*x^2 + b*x + a))^6*a^2*b^6*sqrt(c)*d*e^10 - 367400*(sqrt(c)*x - sqrt(c*x^2
+ b*x + a))^6*a^3*b^4*c^(3/2)*d*e^10 - 300960*(sqrt(c)*x - sqrt(c*x^2 + b*x + a))^6*a^4*b^2*c^(5/2)*d*e^10 + 5
1840*(sqrt(c)*x - sqrt(c*x^2 + b*x + a))^6*a^5*c^(7/2)*d*e^10 + 66870*(sqrt(c)*x - sqrt(c*x^2 + b*x + a))^4*a^
2*b^7*sqrt(c)*d^2*e^9 + 337080*(sqrt(c)*x - sqrt(c*x^2 + b*x + a))^4*a^3*b^5*c^(3/2)*d^2*e^9 + 928800*(sqrt(c)
*x - sqrt(c*x^2 + b*x + a))^4*a^4*b^3*c^(5/2)*d^2*e^9 + 5760*(sqrt(c)*x - sqrt(c*x^2 + b*x + a))^4*a^5*b*c^(7/
2)*d^2*e^9 + 10710*(sqrt(c)*x - sqrt(c*x^2 + b*x + a))^2*a^2*b^8*sqrt(c)*d^3*e^8 - 104760*(sqrt(c)*x - sqrt(c*
x^2 + b*x + a))^2*a^3*b^6*c^(3/2)*d^3*e^8 - 265080*(sqrt(c)*x - sqrt(c*x^2 + b*x + a))^2*a^4*b^4*c^(5/2)*d^3*e
^8 - 556992*(sqrt(c)*x - sqrt(c*x^2 + b*x + a))^2*a^5*b^2*c^(7/2)*d^3*e^8 - 258432*(sqrt(c)*x - sqrt(c*x^2 + b
*x + a))^2*a^6*c^(9/2)*d^3*e^8 + 1050*a^2*b^9*sqrt(c)*d^4*e^7 - 5680*a^3*b^7*c^(3/2)*d^4*e^7 - 3240*a^4*b^5*c^
(5/2)*d^4*e^7 + 42048*a^5*b^3*c^(7/2)*d^4*e^7 - 11392*a^6*b*c^(9/2)*d^4*e^7 - 1386*(sqrt(c)*x - sqrt(c*x^2 + b
*x + a))^7*a^2*b^6*e^11 + 11880*(sqrt(c)*x - sqrt(c*x^2 + b*x + a))^7*a^3*b^4*c*e^11 + 97440*(sqrt(c)*x - sqrt
(c*x^2 + b*x + a))^7*a^4*b^2*c^2*e^11 + 24960*(sqrt(c)*x - sqrt(c*x^2 + b*x + a))^7*a^5*c^3*e^11 - 5058*(sqrt(
c)*x - sqrt(c*x^2 + b*x + a))^5*a^2*b^7*d*e^10 - 190632*(sqrt(c)*x - sqrt(c*x^2 + b*x + a))^5*a^3*b^5*c*d*e^10
- 305760*(sqrt(c)*x - sqrt(c*x^2 + b*x + a))^5*a^4*b^3*c^2*d*e^10 - 293760*(sqrt(c)*x - sqrt(c*x^2 + b*x + a)
)^5*a^5*b*c^3*d*e^10 + 3570*(sqrt(c)*x - sqrt(c*x^2 + b*x + a))^3*a^2*b^8*d^2*e^9 + 58240*(sqrt(c)*x - sqrt(c*
x^2 + b*x + a))^3*a^3*b^6*c*d^2*e^9 + 646200*(sqrt(c)*x - sqrt(c*x^2 + b*x + a))^3*a^4*b^4*c^2*d^2*e^9 + 27552
0*(sqrt(c)*x - sqrt(c*x^2 + b*x + a))^3*a^5*b^2*c^3*d^2*e^9 - 149120*(sqrt(c)*x - sqrt(c*x^2 + b*x + a))^3*a^6
*c^4*d^2*e^9 + 1050*(sqrt(c)*x - sqrt(c*x^2 + b*x + a))*a^2*b^9*d^3*e^8 - 10440*(sqrt(c)*x - sqrt(c*x^2 + b*x
+ a))*a^3*b^7*c*d^3*e^8 + 18120*(sqrt(c)*x - sqrt(c*x^2 + b*x + a))*a^4*b^5*c^2*d^3*e^8 - 195264*(sqrt(c)*x -
sqrt(c*x^2 + b*x + a))*a^5*b^3*c^3*d^3*e^8 - 215424*(sqrt(c)*x - sqrt(c*x^2 + b*x + a))*a^6*b*c^4*d^3*e^8 + 11
2640*(sqrt(c)*x - sqrt(c*x^2 + b*x + a))^6*a^4*b^3*c^(3/2)*e^11 + 61440*(sqrt(c)*x - sqrt(c*x^2 + b*x + a))^6*
a^5*b*c^(5/2)*e^11 - 53010*(sqrt(c)*x - sqrt(c*x^2 + b*x + a))^4*a^3*b^6*sqrt(c)*d*e^10 - 247800*(sqrt(c)*x -
sqrt(c*x^2 + b*x + a))^4*a^4*b^4*c^(3/2)*d*e^10 - 280800*(sqrt(c)*x - sqrt(c*x^2 + b*x + a))^4*a^5*b^2*c^(5/2)
*d*e^10 - 59520*(sqrt(c)*x - sqrt(c*x^2 + b*x + a))^4*a^6*c^(7/2)*d*e^10 - 7140*(sqrt(c)*x - sqrt(c*x^2 + b*x
+ a))^2*a^3*b^7*sqrt(c)*d^2*e^9 + 147240*(sqrt(c)*x - sqrt(c*x^2 + b*x + a))^2*a^4*b^5*c^(3/2)*d^2*e^9 + 25228
8*(sqrt(c)*x - sqrt(c*x^2 + b*x + a))^2*a^5*b^3*c^(5/2)*d^2*e^9 + 163968*(sqrt(c)*x - sqrt(c*x^2 + b*x + a))^2
*a^6*b*c^(7/2)*d^2*e^9 - 1050*a^3*b^8*sqrt(c)*d^3*e^8 + 7270*a^4*b^6*c^(3/2)*d^3*e^8 - 11232*a^5*b^4*c^(5/2)*d
^3*e^8 - 45600*a^6*b^2*c^(7/2)*d^3*e^8 + 1792*a^7*c^(9/2)*d^3*e^8 + 1686*(sqrt(c)*x - sqrt(c*x^2 + b*x + a))^5
*a^3*b^6*e^11 + 42600*(sqrt(c)*x - sqrt(c*x^2 + b*x + a))^5*a^4*b^4*c*e^11 + 128160*(sqrt(c)*x - sqrt(c*x^2 +
b*x + a))^5*a^5*b^2*c^2*e^11 + 24960*(sqrt(c)*x - sqrt(c*x^2 + b*x + a))^5*a^6*c^3*e^11 - 2380*(sqrt(c)*x - sq
rt(c*x^2 + b*x + a))^3*a^3*b^7*d*e^10 - 73800*(sqrt(c)*x - sqrt(c*x^2 + b*x + a))^3*a^4*b^5*c*d*e^10 - 309120*
(sqrt(c)*x - sqrt(c*x^2 + b*x + a))^3*a^5*b^3*c^2*d*e^10 + 30080*(sqrt(c)*x - sqrt(c*x^2 + b*x + a))^3*a^6*b*c
^3*d*e^10 - 1050*(sqrt(c)*x - sqrt(c*x^2 + b*x + a))*a^3*b^8*d^2*e^9 + 8460*(sqrt(c)*x - sqrt(c*x^2 + b*x + a)
)*a^4*b^6*c*d^2*e^9 + 27720*(sqrt(c)*x - sqrt(c*x^2 + b*x + a))*a^5*b^4*c^2*d^2*e^9 + 144768*(sqrt(c)*x - sqrt
(c*x^2 + b*x + a))*a^6*b^2*c^3*d^2*e^9 + 56448*(sqrt(c)*x - sqrt(c*x^2 + b*x + a))*a^7*c^4*d^2*e^9 + 15360*(sq
rt(c)*x - sqrt(c*x^2 + b*x + a))^4*a^4*b^5*sqrt(c)*e^11 + 61440*(sqrt(c)*x - sqrt(c*x^2 + b*x + a))^4*a^5*b^3*
c^(3/2)*e^11 + 92160*(sqrt(c)*x - sqrt(c*x^2 + b*x + a))^4*a^6*b*c^(5/2)*e^11 + 1785*(sqrt(c)*x - sqrt(c*x^2 +
b*x + a))^2*a^4*b^6*sqrt(c)*d*e^10 - 107460*(sqrt(c)*x - sqrt(c*x^2 + b*x + a))^2*a^5*b^4*c^(3/2)*d*e^10 - 95
376*(sqrt(c)*x - sqrt(c*x^2 + b*x + a))^2*a^6*b^2*c^(5/2)*d*e^10 + 20544*(sqrt(c)*x - sqrt(c*x^2 + b*x + a))^2
*a^7*c^(7/2)*d*e^10 + 525*a^4*b^7*sqrt(c)*d^2*e^9 - 4140*a^5*b^5*c^(3/2)*d^2*e^9 + 17136*a^6*b^3*c^(5/2)*d^2*e
^9 + 25536*a^7*b*c^(7/2)*d^2*e^9 + 595*(sqrt(c)*x - sqrt(c*x^2 + b*x + a))^3*a^4*b^6*e^11 + 25620*(sqrt(c)*x -
sqrt(c*x^2 + b*x + a))^3*a^5*b^4*c*e^11 + 58320*(sqrt(c)*x - sqrt(c*x^2 + b*x + a))^3*a^6*b^2*c^2*e^11 + 1504
0*(sqrt(c)*x - sqrt(c*x^2 + b*x + a))^3*a^7*c^3*e^11 + 525*(sqrt(c)*x - sqrt(c*x^2 + b*x + a))*a^4*b^7*d*e^10
- 4140*(sqrt(c)*x - sqrt(c*x^2 + b*x + a))*a^5*b^5*c*d*e^10 - 38160*(sqrt(c)*x - sqrt(c*x^2 + b*x + a))*a^6*b^
3*c^2*d*e^10 - 35904*(sqrt(c)*x - sqrt(c*x^2 + b*x + a))*a^7*b*c^3*d*e^10 + 30720*(sqrt(c)*x - sqrt(c*x^2 + b*
x + a))^2*a^6*b^3*c^(3/2)*e^11 + 12288*(sqrt(c)*x - sqrt(c*x^2 + b*x + a))^2*a^7*b*c^(5/2)*e^11 - 105*a^5*b^6*
sqrt(c)*d*e^10 + 900*a^6*b^4*c^(3/2)*d*e^10 - 11376*a^7*b^2*c^(5/2)*d*e^10 - 5184*a^8*c^(7/2)*d*e^10 - 105*(sq
rt(c)*x - sqrt(c*x^2 + b*x + a))*a^5*b^6*e^11 + 900*(sqrt(c)*x - sqrt(c*x^2 + b*x + a))*a^6*b^4*c*e^11 + 13200
*(sqrt(c)*x - sqrt(c*x^2 + b*x + a))*a^7*b^2*c^2*e^11 + 960*(sqrt(c)*x - sqrt(c*x^2 + b*x + a))*a^8*c^3*e^11 +
3072*a^8*b*c^(5/2)*e^11)/((c^4*d^8*e^4 - 4*b*c^3*d^7*e^5 + 6*b^2*c^2*d^6*e^6 + 4*a*c^3*d^6*e^6 - 4*b^3*c*d^5*
e^7 - 12*a*b*c^2*d^5*e^7 + b^4*d^4*e^8 + 12*a*b^2*c*d^4*e^8 + 6*a^2*c^2*d^4*e^8 - 4*a*b^3*d^3*e^9 - 12*a^2*b*c
*d^3*e^9 + 6*a^2*b^2*d^2*e^10 + 4*a^3*c*d^2*e^10 - 4*a^3*b*d*e^11 + a^4*e^12)*((sqrt(c)*x - sqrt(c*x^2 + b*x +
a))^2*e + 2*(sqrt(c)*x - sqrt(c*x^2 + b*x + a))*sqrt(c)*d + b*d - a*e)^6)

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maple [B]  time = 0.54, size = 28629, normalized size = 70.00 \begin {gather*} \text {output too large to display} \end {gather*}

Verification of antiderivative is not currently implemented for this CAS.

[In]

int((c*x^2+b*x+a)^(3/2)/(e*x+d)^7,x)

[Out]

result too large to display

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

Verification of antiderivative is not currently implemented for this CAS.

[In]

integrate((c*x^2+b*x+a)^(3/2)/(e*x+d)^7,x, algorithm="maxima")

[Out]

Exception raised: ValueError >> Computation failed since Maxima requested additional constraints; using the 'a
ssume' command before evaluation *may* help (example of legal syntax is 'assume(a*e^2-b*d*e>0)', see `assume?`
for more details)Is a*e^2-b*d*e                            +c*d^2 zero or nonzero?

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

Verification of antiderivative is not currently implemented for this CAS.

[In]

int((a + b*x + c*x^2)^(3/2)/(d + e*x)^7,x)

[Out]

int((a + b*x + c*x^2)^(3/2)/(d + e*x)^7, x)

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sympy [F]  time = 0.00, size = 0, normalized size = 0.00 \begin {gather*} \int \frac {\left (a + b x + c x^{2}\right )^{\frac {3}{2}}}{\left (d + e x\right )^{7}}\, dx \end {gather*}

Verification of antiderivative is not currently implemented for this CAS.

[In]

integrate((c*x**2+b*x+a)**(3/2)/(e*x+d)**7,x)

[Out]

Integral((a + b*x + c*x**2)**(3/2)/(d + e*x)**7, x)

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