3.2257 \(\int \frac{(f+g x) (c d^2-b d e-b e^2 x-c e^2 x^2)^{5/2}}{(d+e x)^{9/2}} \, dx\)
Optimal. Leaf size=360 \[ -\frac{(e f-d g) \left (d (c d-b e)-b e^2 x-c e^2 x^2\right )^{7/2}}{e^2 (d+e x)^{9/2} (2 c d-b e)}-\frac{\left (d (c d-b e)-b e^2 x-c e^2 x^2\right )^{5/2} (2 b e g-9 c d g+5 c e f)}{5 e^2 (d+e x)^{5/2} (2 c d-b e)}-\frac{\left (d (c d-b e)-b e^2 x-c e^2 x^2\right )^{3/2} (2 b e g-9 c d g+5 c e f)}{3 e^2 (d+e x)^{3/2}}-\frac{(2 c d-b e) \sqrt{d (c d-b e)-b e^2 x-c e^2 x^2} (2 b e g-9 c d g+5 c e f)}{e^2 \sqrt{d+e x}}+\frac{(2 c d-b e)^{3/2} (2 b e g-9 c d g+5 c e f) \tanh ^{-1}\left (\frac{\sqrt{d (c d-b e)-b e^2 x-c e^2 x^2}}{\sqrt{d+e x} \sqrt{2 c d-b e}}\right )}{e^2} \]
[Out]
-(((2*c*d - b*e)*(5*c*e*f - 9*c*d*g + 2*b*e*g)*Sqrt[d*(c*d - b*e) - b*e^2*x - c*e^2*x^2])/(e^2*Sqrt[d + e*x]))
- ((5*c*e*f - 9*c*d*g + 2*b*e*g)*(d*(c*d - b*e) - b*e^2*x - c*e^2*x^2)^(3/2))/(3*e^2*(d + e*x)^(3/2)) - ((5*c
*e*f - 9*c*d*g + 2*b*e*g)*(d*(c*d - b*e) - b*e^2*x - c*e^2*x^2)^(5/2))/(5*e^2*(2*c*d - b*e)*(d + e*x)^(5/2)) -
((e*f - d*g)*(d*(c*d - b*e) - b*e^2*x - c*e^2*x^2)^(7/2))/(e^2*(2*c*d - b*e)*(d + e*x)^(9/2)) + ((2*c*d - b*e
)^(3/2)*(5*c*e*f - 9*c*d*g + 2*b*e*g)*ArcTanh[Sqrt[d*(c*d - b*e) - b*e^2*x - c*e^2*x^2]/(Sqrt[2*c*d - b*e]*Sqr
t[d + e*x])])/e^2
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Rubi [A] time = 0.609813, antiderivative size = 360, normalized size of antiderivative = 1.,
number of steps used = 6, number of rules used = 4, integrand size = 46, \(\frac{\text{number of rules}}{\text{integrand size}}\) = 0.087, Rules used =
{792, 664, 660, 208} \[ -\frac{(e f-d g) \left (d (c d-b e)-b e^2 x-c e^2 x^2\right )^{7/2}}{e^2 (d+e x)^{9/2} (2 c d-b e)}-\frac{\left (d (c d-b e)-b e^2 x-c e^2 x^2\right )^{5/2} (2 b e g-9 c d g+5 c e f)}{5 e^2 (d+e x)^{5/2} (2 c d-b e)}-\frac{\left (d (c d-b e)-b e^2 x-c e^2 x^2\right )^{3/2} (2 b e g-9 c d g+5 c e f)}{3 e^2 (d+e x)^{3/2}}-\frac{(2 c d-b e) \sqrt{d (c d-b e)-b e^2 x-c e^2 x^2} (2 b e g-9 c d g+5 c e f)}{e^2 \sqrt{d+e x}}+\frac{(2 c d-b e)^{3/2} (2 b e g-9 c d g+5 c e f) \tanh ^{-1}\left (\frac{\sqrt{d (c d-b e)-b e^2 x-c e^2 x^2}}{\sqrt{d+e x} \sqrt{2 c d-b e}}\right )}{e^2} \]
Antiderivative was successfully verified.
[In]
Int[((f + g*x)*(c*d^2 - b*d*e - b*e^2*x - c*e^2*x^2)^(5/2))/(d + e*x)^(9/2),x]
[Out]
-(((2*c*d - b*e)*(5*c*e*f - 9*c*d*g + 2*b*e*g)*Sqrt[d*(c*d - b*e) - b*e^2*x - c*e^2*x^2])/(e^2*Sqrt[d + e*x]))
- ((5*c*e*f - 9*c*d*g + 2*b*e*g)*(d*(c*d - b*e) - b*e^2*x - c*e^2*x^2)^(3/2))/(3*e^2*(d + e*x)^(3/2)) - ((5*c
*e*f - 9*c*d*g + 2*b*e*g)*(d*(c*d - b*e) - b*e^2*x - c*e^2*x^2)^(5/2))/(5*e^2*(2*c*d - b*e)*(d + e*x)^(5/2)) -
((e*f - d*g)*(d*(c*d - b*e) - b*e^2*x - c*e^2*x^2)^(7/2))/(e^2*(2*c*d - b*e)*(d + e*x)^(9/2)) + ((2*c*d - b*e
)^(3/2)*(5*c*e*f - 9*c*d*g + 2*b*e*g)*ArcTanh[Sqrt[d*(c*d - b*e) - b*e^2*x - c*e^2*x^2]/(Sqrt[2*c*d - b*e]*Sqr
t[d + e*x])])/e^2
Rule 792
Int[((d_.) + (e_.)*(x_))^(m_)*((f_.) + (g_.)*(x_))*((a_.) + (b_.)*(x_) + (c_.)*(x_)^2)^(p_), x_Symbol] :> Simp
[((d*g - e*f)*(d + e*x)^m*(a + b*x + c*x^2)^(p + 1))/((2*c*d - b*e)*(m + p + 1)), x] + Dist[(m*(g*(c*d - b*e)
+ c*e*f) + e*(p + 1)*(2*c*f - b*g))/(e*(2*c*d - b*e)*(m + p + 1)), 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] && EqQ[c*d^2 - b*d*e + a*e^2, 0] && ((L
tQ[m, -1] && !IGtQ[m + p + 1, 0]) || (LtQ[m, 0] && LtQ[p, -1]) || EqQ[m + 2*p + 2, 0]) && NeQ[m + p + 1, 0]
Rule 664
Int[((d_.) + (e_.)*(x_))^(m_)*((a_.) + (b_.)*(x_) + (c_.)*(x_)^2)^(p_), x_Symbol] :> Simp[((d + e*x)^(m + 1)*(
a + b*x + c*x^2)^p)/(e*(m + 2*p + 1)), x] - Dist[(p*(2*c*d - b*e))/(e^2*(m + 2*p + 1)), Int[(d + e*x)^(m + 1)*
(a + b*x + c*x^2)^(p - 1), x], x] /; FreeQ[{a, b, c, d, e}, x] && NeQ[b^2 - 4*a*c, 0] && EqQ[c*d^2 - b*d*e + a
*e^2, 0] && GtQ[p, 0] && (LeQ[-2, m, 0] || EqQ[m + p + 1, 0]) && NeQ[m + 2*p + 1, 0] && IntegerQ[2*p]
Rule 660
Int[1/(Sqrt[(d_.) + (e_.)*(x_)]*Sqrt[(a_.) + (b_.)*(x_) + (c_.)*(x_)^2]), x_Symbol] :> Dist[2*e, Subst[Int[1/(
2*c*d - b*e + e^2*x^2), x], x, Sqrt[a + b*x + c*x^2]/Sqrt[d + e*x]], x] /; FreeQ[{a, b, c, d, e}, x] && NeQ[b^
2 - 4*a*c, 0] && EqQ[c*d^2 - b*d*e + a*e^2, 0]
Rule 208
Int[((a_) + (b_.)*(x_)^2)^(-1), x_Symbol] :> Simp[(Rt[-(a/b), 2]*ArcTanh[x/Rt[-(a/b), 2]])/a, x] /; FreeQ[{a,
b}, x] && NegQ[a/b]
Rubi steps
\begin{align*} \int \frac{(f+g x) \left (c d^2-b d e-b e^2 x-c e^2 x^2\right )^{5/2}}{(d+e x)^{9/2}} \, dx &=-\frac{(e f-d g) \left (d (c d-b e)-b e^2 x-c e^2 x^2\right )^{7/2}}{e^2 (2 c d-b e) (d+e x)^{9/2}}-\frac{(5 c e f-9 c d g+2 b e g) \int \frac{\left (c d^2-b d e-b e^2 x-c e^2 x^2\right )^{5/2}}{(d+e x)^{7/2}} \, dx}{2 e (2 c d-b e)}\\ &=-\frac{(5 c e f-9 c d g+2 b e g) \left (d (c d-b e)-b e^2 x-c e^2 x^2\right )^{5/2}}{5 e^2 (2 c d-b e) (d+e x)^{5/2}}-\frac{(e f-d g) \left (d (c d-b e)-b e^2 x-c e^2 x^2\right )^{7/2}}{e^2 (2 c d-b e) (d+e x)^{9/2}}+\frac{((-2 c d+b e) (5 c e f-9 c d g+2 b e g)) \int \frac{\left (c d^2-b d e-b e^2 x-c e^2 x^2\right )^{3/2}}{(d+e x)^{5/2}} \, dx}{2 e (2 c d-b e)}\\ &=-\frac{(5 c e f-9 c d g+2 b e g) \left (d (c d-b e)-b e^2 x-c e^2 x^2\right )^{3/2}}{3 e^2 (d+e x)^{3/2}}-\frac{(5 c e f-9 c d g+2 b e g) \left (d (c d-b e)-b e^2 x-c e^2 x^2\right )^{5/2}}{5 e^2 (2 c d-b e) (d+e x)^{5/2}}-\frac{(e f-d g) \left (d (c d-b e)-b e^2 x-c e^2 x^2\right )^{7/2}}{e^2 (2 c d-b e) (d+e x)^{9/2}}-\frac{((2 c d-b e) (5 c e f-9 c d g+2 b e g)) \int \frac{\sqrt{c d^2-b d e-b e^2 x-c e^2 x^2}}{(d+e x)^{3/2}} \, dx}{2 e}\\ &=-\frac{(2 c d-b e) (5 c e f-9 c d g+2 b e g) \sqrt{d (c d-b e)-b e^2 x-c e^2 x^2}}{e^2 \sqrt{d+e x}}-\frac{(5 c e f-9 c d g+2 b e g) \left (d (c d-b e)-b e^2 x-c e^2 x^2\right )^{3/2}}{3 e^2 (d+e x)^{3/2}}-\frac{(5 c e f-9 c d g+2 b e g) \left (d (c d-b e)-b e^2 x-c e^2 x^2\right )^{5/2}}{5 e^2 (2 c d-b e) (d+e x)^{5/2}}-\frac{(e f-d g) \left (d (c d-b e)-b e^2 x-c e^2 x^2\right )^{7/2}}{e^2 (2 c d-b e) (d+e x)^{9/2}}-\frac{\left ((2 c d-b e)^2 (5 c e f-9 c d g+2 b e g)\right ) \int \frac{1}{\sqrt{d+e x} \sqrt{c d^2-b d e-b e^2 x-c e^2 x^2}} \, dx}{2 e}\\ &=-\frac{(2 c d-b e) (5 c e f-9 c d g+2 b e g) \sqrt{d (c d-b e)-b e^2 x-c e^2 x^2}}{e^2 \sqrt{d+e x}}-\frac{(5 c e f-9 c d g+2 b e g) \left (d (c d-b e)-b e^2 x-c e^2 x^2\right )^{3/2}}{3 e^2 (d+e x)^{3/2}}-\frac{(5 c e f-9 c d g+2 b e g) \left (d (c d-b e)-b e^2 x-c e^2 x^2\right )^{5/2}}{5 e^2 (2 c d-b e) (d+e x)^{5/2}}-\frac{(e f-d g) \left (d (c d-b e)-b e^2 x-c e^2 x^2\right )^{7/2}}{e^2 (2 c d-b e) (d+e x)^{9/2}}-\left ((2 c d-b e)^2 (5 c e f-9 c d g+2 b e g)\right ) \operatorname{Subst}\left (\int \frac{1}{-2 c d e^2+b e^3+e^2 x^2} \, dx,x,\frac{\sqrt{c d^2-b d e-b e^2 x-c e^2 x^2}}{\sqrt{d+e x}}\right )\\ &=-\frac{(2 c d-b e) (5 c e f-9 c d g+2 b e g) \sqrt{d (c d-b e)-b e^2 x-c e^2 x^2}}{e^2 \sqrt{d+e x}}-\frac{(5 c e f-9 c d g+2 b e g) \left (d (c d-b e)-b e^2 x-c e^2 x^2\right )^{3/2}}{3 e^2 (d+e x)^{3/2}}-\frac{(5 c e f-9 c d g+2 b e g) \left (d (c d-b e)-b e^2 x-c e^2 x^2\right )^{5/2}}{5 e^2 (2 c d-b e) (d+e x)^{5/2}}-\frac{(e f-d g) \left (d (c d-b e)-b e^2 x-c e^2 x^2\right )^{7/2}}{e^2 (2 c d-b e) (d+e x)^{9/2}}+\frac{(2 c d-b e)^{3/2} (5 c e f-9 c d g+2 b e g) \tanh ^{-1}\left (\frac{\sqrt{d (c d-b e)-b e^2 x-c e^2 x^2}}{\sqrt{2 c d-b e} \sqrt{d+e x}}\right )}{e^2}\\ \end{align*}
Mathematica [A] time = 0.780806, size = 221, normalized size = 0.61 \[ \frac{((d+e x) (c (d-e x)-b e))^{5/2} \left ((e f-d g) (b e-c d+c e x)-\frac{(d+e x) (2 b e g-9 c d g+5 c e f) \left (\sqrt{c (d-e x)-b e} \left (23 b^2 e^2+b c e (11 e x-81 d)+c^2 \left (73 d^2-16 d e x+3 e^2 x^2\right )\right )-15 (2 c d-b e)^{5/2} \tanh ^{-1}\left (\frac{\sqrt{-b e+c d-c e x}}{\sqrt{2 c d-b e}}\right )\right )}{15 (c (d-e x)-b e)^{5/2}}\right )}{e^2 (d+e x)^{7/2} (2 c d-b e)} \]
Antiderivative was successfully verified.
[In]
Integrate[((f + g*x)*(c*d^2 - b*d*e - b*e^2*x - c*e^2*x^2)^(5/2))/(d + e*x)^(9/2),x]
[Out]
(((d + e*x)*(-(b*e) + c*(d - e*x)))^(5/2)*((e*f - d*g)*(-(c*d) + b*e + c*e*x) - ((5*c*e*f - 9*c*d*g + 2*b*e*g)
*(d + e*x)*(Sqrt[-(b*e) + c*(d - e*x)]*(23*b^2*e^2 + b*c*e*(-81*d + 11*e*x) + c^2*(73*d^2 - 16*d*e*x + 3*e^2*x
^2)) - 15*(2*c*d - b*e)^(5/2)*ArcTanh[Sqrt[c*d - b*e - c*e*x]/Sqrt[2*c*d - b*e]]))/(15*(-(b*e) + c*(d - e*x))^
(5/2))))/(e^2*(2*c*d - b*e)*(d + e*x)^(7/2))
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Maple [B] time = 0.027, size = 1136, normalized size = 3.2 \begin{align*} \text{result too large to display} \end{align*}
Verification of antiderivative is not currently implemented for this CAS.
[In]
int((g*x+f)*(-c*e^2*x^2-b*e^2*x-b*d*e+c*d^2)^(5/2)/(e*x+d)^(9/2),x)
[Out]
-1/15*(-c*e^2*x^2-b*e^2*x-b*d*e+c*d^2)^(1/2)*(300*arctan((-c*e*x-b*e+c*d)^(1/2)/(b*e-2*c*d)^(1/2))*x*c^3*d^2*e
^2*f+660*arctan((-c*e*x-b*e+c*d)^(1/2)/(b*e-2*c*d)^(1/2))*b*c^2*d^3*e*g-10*x^2*c^2*e^3*f*(-c*e*x-b*e+c*d)^(1/2
)*(b*e-2*c*d)^(1/2)-46*x*b^2*e^3*g*(-c*e*x-b*e+c*d)^(1/2)*(b*e-2*c*d)^(1/2)-540*arctan((-c*e*x-b*e+c*d)^(1/2)/
(b*e-2*c*d)^(1/2))*x*c^3*d^3*e*g+15*b^2*e^3*f*(-c*e*x-b*e+c*d)^(1/2)*(b*e-2*c*d)^(1/2)+75*arctan((-c*e*x-b*e+c
*d)^(1/2)/(b*e-2*c*d)^(1/2))*b^2*c*d*e^3*f-300*arctan((-c*e*x-b*e+c*d)^(1/2)/(b*e-2*c*d)^(1/2))*b*c^2*d^2*e^2*
f-255*arctan((-c*e*x-b*e+c*d)^(1/2)/(b*e-2*c*d)^(1/2))*b^2*c*d^2*e^2*g+75*arctan((-c*e*x-b*e+c*d)^(1/2)/(b*e-2
*c*d)^(1/2))*x*b^2*c*e^4*f-6*x^3*c^2*e^3*g*(-c*e*x-b*e+c*d)^(1/2)*(b*e-2*c*d)^(1/2)-61*b^2*d*e^2*g*(-c*e*x-b*e
+c*d)^(1/2)*(b*e-2*c*d)^(1/2)+190*c^2*d^2*e*f*(-c*e*x-b*e+c*d)^(1/2)*(b*e-2*c*d)^(1/2)+210*x*b*c*d*e^2*g*(-c*e
*x-b*e+c*d)^(1/2)*(b*e-2*c*d)^(1/2)-540*arctan((-c*e*x-b*e+c*d)^(1/2)/(b*e-2*c*d)^(1/2))*c^3*d^4*g-336*c^2*d^3
*g*(-c*e*x-b*e+c*d)^(1/2)*(b*e-2*c*d)^(1/2)+300*arctan((-c*e*x-b*e+c*d)^(1/2)/(b*e-2*c*d)^(1/2))*c^3*d^3*e*f+3
0*arctan((-c*e*x-b*e+c*d)^(1/2)/(b*e-2*c*d)^(1/2))*b^3*d*e^3*g+30*arctan((-c*e*x-b*e+c*d)^(1/2)/(b*e-2*c*d)^(1
/2))*x*b^3*e^4*g-22*x^2*b*c*e^3*g*(-c*e*x-b*e+c*d)^(1/2)*(b*e-2*c*d)^(1/2)+36*x^2*c^2*d*e^2*g*(-c*e*x-b*e+c*d)
^(1/2)*(b*e-2*c*d)^(1/2)-70*x*b*c*e^3*f*(-c*e*x-b*e+c*d)^(1/2)*(b*e-2*c*d)^(1/2)-234*x*c^2*d^2*e*g*(-c*e*x-b*e
+c*d)^(1/2)*(b*e-2*c*d)^(1/2)+120*x*c^2*d*e^2*f*(-c*e*x-b*e+c*d)^(1/2)*(b*e-2*c*d)^(1/2)+292*b*c*d^2*e*g*(-c*e
*x-b*e+c*d)^(1/2)*(b*e-2*c*d)^(1/2)-130*b*c*d*e^2*f*(-c*e*x-b*e+c*d)^(1/2)*(b*e-2*c*d)^(1/2)+660*arctan((-c*e*
x-b*e+c*d)^(1/2)/(b*e-2*c*d)^(1/2))*x*b*c^2*d^2*e^2*g-255*arctan((-c*e*x-b*e+c*d)^(1/2)/(b*e-2*c*d)^(1/2))*x*b
^2*c*d*e^3*g-300*arctan((-c*e*x-b*e+c*d)^(1/2)/(b*e-2*c*d)^(1/2))*x*b*c^2*d*e^3*f)/(e*x+d)^(3/2)/(-c*e*x-b*e+c
*d)^(1/2)/e^2/(b*e-2*c*d)^(1/2)
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Maxima [F] time = 0., size = 0, normalized size = 0. \begin{align*} \int \frac{{\left (-c e^{2} x^{2} - b e^{2} x + c d^{2} - b d e\right )}^{\frac{5}{2}}{\left (g x + f\right )}}{{\left (e x + d\right )}^{\frac{9}{2}}}\,{d x} \end{align*}
Verification of antiderivative is not currently implemented for this CAS.
[In]
integrate((g*x+f)*(-c*e^2*x^2-b*e^2*x-b*d*e+c*d^2)^(5/2)/(e*x+d)^(9/2),x, algorithm="maxima")
[Out]
integrate((-c*e^2*x^2 - b*e^2*x + c*d^2 - b*d*e)^(5/2)*(g*x + f)/(e*x + d)^(9/2), x)
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Fricas [A] time = 1.55463, size = 2107, normalized size = 5.85 \begin{align*} \text{result too large to display} \end{align*}
Verification of antiderivative is not currently implemented for this CAS.
[In]
integrate((g*x+f)*(-c*e^2*x^2-b*e^2*x-b*d*e+c*d^2)^(5/2)/(e*x+d)^(9/2),x, algorithm="fricas")
[Out]
[-1/30*(15*((5*(2*c^2*d*e^3 - b*c*e^4)*f - (18*c^2*d^2*e^2 - 13*b*c*d*e^3 + 2*b^2*e^4)*g)*x^2 + 5*(2*c^2*d^3*e
- b*c*d^2*e^2)*f - (18*c^2*d^4 - 13*b*c*d^3*e + 2*b^2*d^2*e^2)*g + 2*(5*(2*c^2*d^2*e^2 - b*c*d*e^3)*f - (18*c
^2*d^3*e - 13*b*c*d^2*e^2 + 2*b^2*d*e^3)*g)*x)*sqrt(2*c*d - b*e)*log(-(c*e^2*x^2 - 3*c*d^2 + 2*b*d*e - 2*(c*d*
e - b*e^2)*x + 2*sqrt(-c*e^2*x^2 - b*e^2*x + c*d^2 - b*d*e)*sqrt(2*c*d - b*e)*sqrt(e*x + d))/(e^2*x^2 + 2*d*e*
x + d^2)) - 2*(6*c^2*e^3*g*x^3 + 2*(5*c^2*e^3*f - (18*c^2*d*e^2 - 11*b*c*e^3)*g)*x^2 - 5*(38*c^2*d^2*e - 26*b*
c*d*e^2 + 3*b^2*e^3)*f + (336*c^2*d^3 - 292*b*c*d^2*e + 61*b^2*d*e^2)*g - 2*(5*(12*c^2*d*e^2 - 7*b*c*e^3)*f -
(117*c^2*d^2*e - 105*b*c*d*e^2 + 23*b^2*e^3)*g)*x)*sqrt(-c*e^2*x^2 - b*e^2*x + c*d^2 - b*d*e)*sqrt(e*x + d))/(
e^4*x^2 + 2*d*e^3*x + d^2*e^2), 1/15*(15*((5*(2*c^2*d*e^3 - b*c*e^4)*f - (18*c^2*d^2*e^2 - 13*b*c*d*e^3 + 2*b^
2*e^4)*g)*x^2 + 5*(2*c^2*d^3*e - b*c*d^2*e^2)*f - (18*c^2*d^4 - 13*b*c*d^3*e + 2*b^2*d^2*e^2)*g + 2*(5*(2*c^2*
d^2*e^2 - b*c*d*e^3)*f - (18*c^2*d^3*e - 13*b*c*d^2*e^2 + 2*b^2*d*e^3)*g)*x)*sqrt(-2*c*d + b*e)*arctan(sqrt(-c
*e^2*x^2 - b*e^2*x + c*d^2 - b*d*e)*sqrt(-2*c*d + b*e)*sqrt(e*x + d)/(c*e^2*x^2 + b*e^2*x - c*d^2 + b*d*e)) +
(6*c^2*e^3*g*x^3 + 2*(5*c^2*e^3*f - (18*c^2*d*e^2 - 11*b*c*e^3)*g)*x^2 - 5*(38*c^2*d^2*e - 26*b*c*d*e^2 + 3*b^
2*e^3)*f + (336*c^2*d^3 - 292*b*c*d^2*e + 61*b^2*d*e^2)*g - 2*(5*(12*c^2*d*e^2 - 7*b*c*e^3)*f - (117*c^2*d^2*e
- 105*b*c*d*e^2 + 23*b^2*e^3)*g)*x)*sqrt(-c*e^2*x^2 - b*e^2*x + c*d^2 - b*d*e)*sqrt(e*x + d))/(e^4*x^2 + 2*d*
e^3*x + d^2*e^2)]
________________________________________________________________________________________
Sympy [F(-1)] time = 0., size = 0, normalized size = 0. \begin{align*} \text{Timed out} \end{align*}
Verification of antiderivative is not currently implemented for this CAS.
[In]
integrate((g*x+f)*(-c*e**2*x**2-b*e**2*x-b*d*e+c*d**2)**(5/2)/(e*x+d)**(9/2),x)
[Out]
Timed out
________________________________________________________________________________________
Giac [F(-1)] time = 0., size = 0, normalized size = 0. \begin{align*} \text{Timed out} \end{align*}
Verification of antiderivative is not currently implemented for this CAS.
[In]
integrate((g*x+f)*(-c*e^2*x^2-b*e^2*x-b*d*e+c*d^2)^(5/2)/(e*x+d)^(9/2),x, algorithm="giac")
[Out]
Timed out