3.1.39 \(\int F^{c (a+b x)} (d+e x)^{7/2} \, dx\) [39]

Optimal. Leaf size=208 \[ \frac {105 e^{7/2} F^{c \left (a-\frac {b d}{e}\right )} \sqrt {\pi } \text {erfi}\left (\frac {\sqrt {b} \sqrt {c} \sqrt {d+e x} \sqrt {\log (F)}}{\sqrt {e}}\right )}{16 b^{9/2} c^{9/2} \log ^{\frac {9}{2}}(F)}-\frac {105 e^3 F^{c (a+b x)} \sqrt {d+e x}}{8 b^4 c^4 \log ^4(F)}+\frac {35 e^2 F^{c (a+b x)} (d+e x)^{3/2}}{4 b^3 c^3 \log ^3(F)}-\frac {7 e F^{c (a+b x)} (d+e x)^{5/2}}{2 b^2 c^2 \log ^2(F)}+\frac {F^{c (a+b x)} (d+e x)^{7/2}}{b c \log (F)} \]

[Out]

35/4*e^2*F^(c*(b*x+a))*(e*x+d)^(3/2)/b^3/c^3/ln(F)^3-7/2*e*F^(c*(b*x+a))*(e*x+d)^(5/2)/b^2/c^2/ln(F)^2+F^(c*(b
*x+a))*(e*x+d)^(7/2)/b/c/ln(F)+105/16*e^(7/2)*F^(c*(a-b*d/e))*erfi(b^(1/2)*c^(1/2)*(e*x+d)^(1/2)*ln(F)^(1/2)/e
^(1/2))*Pi^(1/2)/b^(9/2)/c^(9/2)/ln(F)^(9/2)-105/8*e^3*F^(c*(b*x+a))*(e*x+d)^(1/2)/b^4/c^4/ln(F)^4

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Rubi [A]
time = 0.20, antiderivative size = 208, normalized size of antiderivative = 1.00, number of steps used = 6, number of rules used = 3, integrand size = 19, \(\frac {\text {number of rules}}{\text {integrand size}}\) = 0.158, Rules used = {2207, 2211, 2235} \begin {gather*} \frac {105 \sqrt {\pi } e^{7/2} F^{c \left (a-\frac {b d}{e}\right )} \text {Erfi}\left (\frac {\sqrt {b} \sqrt {c} \sqrt {\log (F)} \sqrt {d+e x}}{\sqrt {e}}\right )}{16 b^{9/2} c^{9/2} \log ^{\frac {9}{2}}(F)}-\frac {105 e^3 \sqrt {d+e x} F^{c (a+b x)}}{8 b^4 c^4 \log ^4(F)}+\frac {35 e^2 (d+e x)^{3/2} F^{c (a+b x)}}{4 b^3 c^3 \log ^3(F)}-\frac {7 e (d+e x)^{5/2} F^{c (a+b x)}}{2 b^2 c^2 \log ^2(F)}+\frac {(d+e x)^{7/2} F^{c (a+b x)}}{b c \log (F)} \end {gather*}

Antiderivative was successfully verified.

[In]

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

[Out]

(105*e^(7/2)*F^(c*(a - (b*d)/e))*Sqrt[Pi]*Erfi[(Sqrt[b]*Sqrt[c]*Sqrt[d + e*x]*Sqrt[Log[F]])/Sqrt[e]])/(16*b^(9
/2)*c^(9/2)*Log[F]^(9/2)) - (105*e^3*F^(c*(a + b*x))*Sqrt[d + e*x])/(8*b^4*c^4*Log[F]^4) + (35*e^2*F^(c*(a + b
*x))*(d + e*x)^(3/2))/(4*b^3*c^3*Log[F]^3) - (7*e*F^(c*(a + b*x))*(d + e*x)^(5/2))/(2*b^2*c^2*Log[F]^2) + (F^(
c*(a + b*x))*(d + e*x)^(7/2))/(b*c*Log[F])

Rule 2207

Int[((b_.)*(F_)^((g_.)*((e_.) + (f_.)*(x_))))^(n_.)*((c_.) + (d_.)*(x_))^(m_.), x_Symbol] :> Simp[(c + d*x)^m*
((b*F^(g*(e + f*x)))^n/(f*g*n*Log[F])), x] - Dist[d*(m/(f*g*n*Log[F])), Int[(c + d*x)^(m - 1)*(b*F^(g*(e + f*x
)))^n, x], x] /; FreeQ[{F, b, c, d, e, f, g, n}, x] && GtQ[m, 0] && IntegerQ[2*m] &&  !TrueQ[$UseGamma]

Rule 2211

Int[(F_)^((g_.)*((e_.) + (f_.)*(x_)))/Sqrt[(c_.) + (d_.)*(x_)], x_Symbol] :> Dist[2/d, Subst[Int[F^(g*(e - c*(
f/d)) + f*g*(x^2/d)), x], x, Sqrt[c + d*x]], x] /; FreeQ[{F, c, d, e, f, g}, x] &&  !TrueQ[$UseGamma]

Rule 2235

Int[(F_)^((a_.) + (b_.)*((c_.) + (d_.)*(x_))^2), x_Symbol] :> Simp[F^a*Sqrt[Pi]*(Erfi[(c + d*x)*Rt[b*Log[F], 2
]]/(2*d*Rt[b*Log[F], 2])), x] /; FreeQ[{F, a, b, c, d}, x] && PosQ[b]

Rubi steps

\begin {align*} \int F^{c (a+b x)} (d+e x)^{7/2} \, dx &=\frac {F^{c (a+b x)} (d+e x)^{7/2}}{b c \log (F)}-\frac {(7 e) \int F^{c (a+b x)} (d+e x)^{5/2} \, dx}{2 b c \log (F)}\\ &=-\frac {7 e F^{c (a+b x)} (d+e x)^{5/2}}{2 b^2 c^2 \log ^2(F)}+\frac {F^{c (a+b x)} (d+e x)^{7/2}}{b c \log (F)}+\frac {\left (35 e^2\right ) \int F^{c (a+b x)} (d+e x)^{3/2} \, dx}{4 b^2 c^2 \log ^2(F)}\\ &=\frac {35 e^2 F^{c (a+b x)} (d+e x)^{3/2}}{4 b^3 c^3 \log ^3(F)}-\frac {7 e F^{c (a+b x)} (d+e x)^{5/2}}{2 b^2 c^2 \log ^2(F)}+\frac {F^{c (a+b x)} (d+e x)^{7/2}}{b c \log (F)}-\frac {\left (105 e^3\right ) \int F^{c (a+b x)} \sqrt {d+e x} \, dx}{8 b^3 c^3 \log ^3(F)}\\ &=-\frac {105 e^3 F^{c (a+b x)} \sqrt {d+e x}}{8 b^4 c^4 \log ^4(F)}+\frac {35 e^2 F^{c (a+b x)} (d+e x)^{3/2}}{4 b^3 c^3 \log ^3(F)}-\frac {7 e F^{c (a+b x)} (d+e x)^{5/2}}{2 b^2 c^2 \log ^2(F)}+\frac {F^{c (a+b x)} (d+e x)^{7/2}}{b c \log (F)}+\frac {\left (105 e^4\right ) \int \frac {F^{c (a+b x)}}{\sqrt {d+e x}} \, dx}{16 b^4 c^4 \log ^4(F)}\\ &=-\frac {105 e^3 F^{c (a+b x)} \sqrt {d+e x}}{8 b^4 c^4 \log ^4(F)}+\frac {35 e^2 F^{c (a+b x)} (d+e x)^{3/2}}{4 b^3 c^3 \log ^3(F)}-\frac {7 e F^{c (a+b x)} (d+e x)^{5/2}}{2 b^2 c^2 \log ^2(F)}+\frac {F^{c (a+b x)} (d+e x)^{7/2}}{b c \log (F)}+\frac {\left (105 e^3\right ) \text {Subst}\left (\int F^{c \left (a-\frac {b d}{e}\right )+\frac {b c x^2}{e}} \, dx,x,\sqrt {d+e x}\right )}{8 b^4 c^4 \log ^4(F)}\\ &=\frac {105 e^{7/2} F^{c \left (a-\frac {b d}{e}\right )} \sqrt {\pi } \text {erfi}\left (\frac {\sqrt {b} \sqrt {c} \sqrt {d+e x} \sqrt {\log (F)}}{\sqrt {e}}\right )}{16 b^{9/2} c^{9/2} \log ^{\frac {9}{2}}(F)}-\frac {105 e^3 F^{c (a+b x)} \sqrt {d+e x}}{8 b^4 c^4 \log ^4(F)}+\frac {35 e^2 F^{c (a+b x)} (d+e x)^{3/2}}{4 b^3 c^3 \log ^3(F)}-\frac {7 e F^{c (a+b x)} (d+e x)^{5/2}}{2 b^2 c^2 \log ^2(F)}+\frac {F^{c (a+b x)} (d+e x)^{7/2}}{b c \log (F)}\\ \end {align*}

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Mathematica [A]
time = 0.15, size = 72, normalized size = 0.35 \begin {gather*} \frac {e^4 F^{c \left (a-\frac {b d}{e}\right )} \Gamma \left (\frac {9}{2},-\frac {b c (d+e x) \log (F)}{e}\right ) \sqrt {-\frac {b c (d+e x) \log (F)}{e}}}{b^5 c^5 \sqrt {d+e x} \log ^5(F)} \end {gather*}

Antiderivative was successfully verified.

[In]

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

[Out]

(e^4*F^(c*(a - (b*d)/e))*Gamma[9/2, -((b*c*(d + e*x)*Log[F])/e)]*Sqrt[-((b*c*(d + e*x)*Log[F])/e)])/(b^5*c^5*S
qrt[d + e*x]*Log[F]^5)

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Maple [F]
time = 0.01, size = 0, normalized size = 0.00 \[\int F^{c \left (b x +a \right )} \left (e x +d \right )^{\frac {7}{2}}\, dx\]

Verification of antiderivative is not currently implemented for this CAS.

[In]

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

[Out]

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

[Out]

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

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Fricas [A]
time = 0.36, size = 224, normalized size = 1.08 \begin {gather*} \frac {2 \, {\left (8 \, {\left (b^{4} c^{4} x^{3} e^{3} + 3 \, b^{4} c^{4} d x^{2} e^{2} + 3 \, b^{4} c^{4} d^{2} x e + b^{4} c^{4} d^{3}\right )} \log \left (F\right )^{4} - 105 \, b c e^{3} \log \left (F\right ) - 28 \, {\left (b^{3} c^{3} x^{2} e^{3} + 2 \, b^{3} c^{3} d x e^{2} + b^{3} c^{3} d^{2} e\right )} \log \left (F\right )^{3} + 70 \, {\left (b^{2} c^{2} x e^{3} + b^{2} c^{2} d e^{2}\right )} \log \left (F\right )^{2}\right )} \sqrt {x e + d} F^{b c x + a c} - \frac {105 \, \sqrt {\pi } \sqrt {-b c e^{\left (-1\right )} \log \left (F\right )} \operatorname {erf}\left (\sqrt {-b c e^{\left (-1\right )} \log \left (F\right )} \sqrt {x e + d}\right ) e^{4}}{F^{{\left (b c d - a c e\right )} e^{\left (-1\right )}}}}{16 \, b^{5} c^{5} \log \left (F\right )^{5}} \end {gather*}

Verification of antiderivative is not currently implemented for this CAS.

[In]

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

[Out]

1/16*(2*(8*(b^4*c^4*x^3*e^3 + 3*b^4*c^4*d*x^2*e^2 + 3*b^4*c^4*d^2*x*e + b^4*c^4*d^3)*log(F)^4 - 105*b*c*e^3*lo
g(F) - 28*(b^3*c^3*x^2*e^3 + 2*b^3*c^3*d*x*e^2 + b^3*c^3*d^2*e)*log(F)^3 + 70*(b^2*c^2*x*e^3 + b^2*c^2*d*e^2)*
log(F)^2)*sqrt(x*e + d)*F^(b*c*x + a*c) - 105*sqrt(pi)*sqrt(-b*c*e^(-1)*log(F))*erf(sqrt(-b*c*e^(-1)*log(F))*s
qrt(x*e + d))*e^4/F^((b*c*d - a*c*e)*e^(-1)))/(b^5*c^5*log(F)^5)

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

[Out]

Exception raised: SystemError >> excessive stack use: stack is 3876 deep

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Giac [B] Leaf count of result is larger than twice the leaf count of optimal. 1091 vs. \(2 (176) = 352\).
time = 2.59, size = 1091, normalized size = 5.25 \begin {gather*} -\frac {1}{16} \, {\left (\frac {16 \, \sqrt {\pi } d^{4} \operatorname {erf}\left (-\sqrt {-b c e \log \left (F\right )} \sqrt {x e + d} e^{\left (-1\right )}\right ) e^{\left (-{\left (b c d \log \left (F\right ) - a c e \log \left (F\right )\right )} e^{\left (-1\right )} + 1\right )}}{\sqrt {-b c e \log \left (F\right )}} - 32 \, d^{3} {\left (\frac {\sqrt {\pi } {\left (2 \, b c d \log \left (F\right ) + e\right )} \operatorname {erf}\left (-\sqrt {-b c e \log \left (F\right )} \sqrt {x e + d} e^{\left (-1\right )}\right ) e^{\left (-{\left (b c d \log \left (F\right ) - a c e \log \left (F\right )\right )} e^{\left (-1\right )} + 1\right )}}{\sqrt {-b c e \log \left (F\right )} b c \log \left (F\right )} + \frac {2 \, \sqrt {x e + d} e^{\left ({\left ({\left (x e + d\right )} b c \log \left (F\right ) - b c d \log \left (F\right ) + a c e \log \left (F\right )\right )} e^{\left (-1\right )} + 1\right )}}{b c \log \left (F\right )}\right )} + 24 \, d^{2} {\left (\frac {\sqrt {\pi } {\left (4 \, b^{2} c^{2} d^{2} \log \left (F\right )^{2} + 4 \, b c d e \log \left (F\right ) + 3 \, e^{2}\right )} \operatorname {erf}\left (-\sqrt {-b c e \log \left (F\right )} \sqrt {x e + d} e^{\left (-1\right )}\right ) e^{\left (-{\left (b c d \log \left (F\right ) - a c e \log \left (F\right ) + 2 \, e\right )} e^{\left (-1\right )} + 1\right )}}{\sqrt {-b c e \log \left (F\right )} b^{2} c^{2} \log \left (F\right )^{2}} - \frac {2 \, {\left (2 \, {\left (x e + d\right )}^{\frac {3}{2}} b c e \log \left (F\right ) - 4 \, \sqrt {x e + d} b c d e \log \left (F\right ) - 3 \, \sqrt {x e + d} e^{2}\right )} e^{\left ({\left ({\left (x e + d\right )} b c \log \left (F\right ) - b c d \log \left (F\right ) + a c e \log \left (F\right ) - 2 \, e\right )} e^{\left (-1\right )}\right )}}{b^{2} c^{2} \log \left (F\right )^{2}}\right )} e^{2} - 8 \, d {\left (\frac {\sqrt {\pi } {\left (8 \, b^{3} c^{3} d^{3} \log \left (F\right )^{3} + 12 \, b^{2} c^{2} d^{2} e \log \left (F\right )^{2} + 18 \, b c d e^{2} \log \left (F\right ) + 15 \, e^{3}\right )} \operatorname {erf}\left (-\sqrt {-b c e \log \left (F\right )} \sqrt {x e + d} e^{\left (-1\right )}\right ) e^{\left (-{\left (b c d \log \left (F\right ) - a c e \log \left (F\right ) + 3 \, e\right )} e^{\left (-1\right )} + 1\right )}}{\sqrt {-b c e \log \left (F\right )} b^{3} c^{3} \log \left (F\right )^{3}} + \frac {2 \, {\left (4 \, {\left (x e + d\right )}^{\frac {5}{2}} b^{2} c^{2} e \log \left (F\right )^{2} - 12 \, {\left (x e + d\right )}^{\frac {3}{2}} b^{2} c^{2} d e \log \left (F\right )^{2} + 12 \, \sqrt {x e + d} b^{2} c^{2} d^{2} e \log \left (F\right )^{2} - 10 \, {\left (x e + d\right )}^{\frac {3}{2}} b c e^{2} \log \left (F\right ) + 18 \, \sqrt {x e + d} b c d e^{2} \log \left (F\right ) + 15 \, \sqrt {x e + d} e^{3}\right )} e^{\left ({\left ({\left (x e + d\right )} b c \log \left (F\right ) - b c d \log \left (F\right ) + a c e \log \left (F\right ) - 3 \, e\right )} e^{\left (-1\right )}\right )}}{b^{3} c^{3} \log \left (F\right )^{3}}\right )} e^{3} + {\left (\frac {\sqrt {\pi } {\left (16 \, b^{4} c^{4} d^{4} \log \left (F\right )^{4} + 32 \, b^{3} c^{3} d^{3} e \log \left (F\right )^{3} + 72 \, b^{2} c^{2} d^{2} e^{2} \log \left (F\right )^{2} + 120 \, b c d e^{3} \log \left (F\right ) + 105 \, e^{4}\right )} \operatorname {erf}\left (-\sqrt {-b c e \log \left (F\right )} \sqrt {x e + d} e^{\left (-1\right )}\right ) e^{\left (-{\left (b c d \log \left (F\right ) - a c e \log \left (F\right ) + 4 \, e\right )} e^{\left (-1\right )} + 1\right )}}{\sqrt {-b c e \log \left (F\right )} b^{4} c^{4} \log \left (F\right )^{4}} - \frac {2 \, {\left (8 \, {\left (x e + d\right )}^{\frac {7}{2}} b^{3} c^{3} e \log \left (F\right )^{3} - 32 \, {\left (x e + d\right )}^{\frac {5}{2}} b^{3} c^{3} d e \log \left (F\right )^{3} + 48 \, {\left (x e + d\right )}^{\frac {3}{2}} b^{3} c^{3} d^{2} e \log \left (F\right )^{3} - 32 \, \sqrt {x e + d} b^{3} c^{3} d^{3} e \log \left (F\right )^{3} - 28 \, {\left (x e + d\right )}^{\frac {5}{2}} b^{2} c^{2} e^{2} \log \left (F\right )^{2} + 80 \, {\left (x e + d\right )}^{\frac {3}{2}} b^{2} c^{2} d e^{2} \log \left (F\right )^{2} - 72 \, \sqrt {x e + d} b^{2} c^{2} d^{2} e^{2} \log \left (F\right )^{2} + 70 \, {\left (x e + d\right )}^{\frac {3}{2}} b c e^{3} \log \left (F\right ) - 120 \, \sqrt {x e + d} b c d e^{3} \log \left (F\right ) - 105 \, \sqrt {x e + d} e^{4}\right )} e^{\left ({\left ({\left (x e + d\right )} b c \log \left (F\right ) - b c d \log \left (F\right ) + a c e \log \left (F\right ) - 4 \, e\right )} e^{\left (-1\right )}\right )}}{b^{4} c^{4} \log \left (F\right )^{4}}\right )} e^{4}\right )} e^{\left (-1\right )} \end {gather*}

Verification of antiderivative is not currently implemented for this CAS.

[In]

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

[Out]

-1/16*(16*sqrt(pi)*d^4*erf(-sqrt(-b*c*e*log(F))*sqrt(x*e + d)*e^(-1))*e^(-(b*c*d*log(F) - a*c*e*log(F))*e^(-1)
+ 1)/sqrt(-b*c*e*log(F)) - 32*d^3*(sqrt(pi)*(2*b*c*d*log(F) + e)*erf(-sqrt(-b*c*e*log(F))*sqrt(x*e + d)*e^(-1
))*e^(-(b*c*d*log(F) - a*c*e*log(F))*e^(-1) + 1)/(sqrt(-b*c*e*log(F))*b*c*log(F)) + 2*sqrt(x*e + d)*e^(((x*e +
d)*b*c*log(F) - b*c*d*log(F) + a*c*e*log(F))*e^(-1) + 1)/(b*c*log(F))) + 24*d^2*(sqrt(pi)*(4*b^2*c^2*d^2*log(
F)^2 + 4*b*c*d*e*log(F) + 3*e^2)*erf(-sqrt(-b*c*e*log(F))*sqrt(x*e + d)*e^(-1))*e^(-(b*c*d*log(F) - a*c*e*log(
F) + 2*e)*e^(-1) + 1)/(sqrt(-b*c*e*log(F))*b^2*c^2*log(F)^2) - 2*(2*(x*e + d)^(3/2)*b*c*e*log(F) - 4*sqrt(x*e
+ d)*b*c*d*e*log(F) - 3*sqrt(x*e + d)*e^2)*e^(((x*e + d)*b*c*log(F) - b*c*d*log(F) + a*c*e*log(F) - 2*e)*e^(-1
))/(b^2*c^2*log(F)^2))*e^2 - 8*d*(sqrt(pi)*(8*b^3*c^3*d^3*log(F)^3 + 12*b^2*c^2*d^2*e*log(F)^2 + 18*b*c*d*e^2*
log(F) + 15*e^3)*erf(-sqrt(-b*c*e*log(F))*sqrt(x*e + d)*e^(-1))*e^(-(b*c*d*log(F) - a*c*e*log(F) + 3*e)*e^(-1)
+ 1)/(sqrt(-b*c*e*log(F))*b^3*c^3*log(F)^3) + 2*(4*(x*e + d)^(5/2)*b^2*c^2*e*log(F)^2 - 12*(x*e + d)^(3/2)*b^
2*c^2*d*e*log(F)^2 + 12*sqrt(x*e + d)*b^2*c^2*d^2*e*log(F)^2 - 10*(x*e + d)^(3/2)*b*c*e^2*log(F) + 18*sqrt(x*e
+ d)*b*c*d*e^2*log(F) + 15*sqrt(x*e + d)*e^3)*e^(((x*e + d)*b*c*log(F) - b*c*d*log(F) + a*c*e*log(F) - 3*e)*e
^(-1))/(b^3*c^3*log(F)^3))*e^3 + (sqrt(pi)*(16*b^4*c^4*d^4*log(F)^4 + 32*b^3*c^3*d^3*e*log(F)^3 + 72*b^2*c^2*d
^2*e^2*log(F)^2 + 120*b*c*d*e^3*log(F) + 105*e^4)*erf(-sqrt(-b*c*e*log(F))*sqrt(x*e + d)*e^(-1))*e^(-(b*c*d*lo
g(F) - a*c*e*log(F) + 4*e)*e^(-1) + 1)/(sqrt(-b*c*e*log(F))*b^4*c^4*log(F)^4) - 2*(8*(x*e + d)^(7/2)*b^3*c^3*e
*log(F)^3 - 32*(x*e + d)^(5/2)*b^3*c^3*d*e*log(F)^3 + 48*(x*e + d)^(3/2)*b^3*c^3*d^2*e*log(F)^3 - 32*sqrt(x*e
+ d)*b^3*c^3*d^3*e*log(F)^3 - 28*(x*e + d)^(5/2)*b^2*c^2*e^2*log(F)^2 + 80*(x*e + d)^(3/2)*b^2*c^2*d*e^2*log(F
)^2 - 72*sqrt(x*e + d)*b^2*c^2*d^2*e^2*log(F)^2 + 70*(x*e + d)^(3/2)*b*c*e^3*log(F) - 120*sqrt(x*e + d)*b*c*d*
e^3*log(F) - 105*sqrt(x*e + d)*e^4)*e^(((x*e + d)*b*c*log(F) - b*c*d*log(F) + a*c*e*log(F) - 4*e)*e^(-1))/(b^4
*c^4*log(F)^4))*e^4)*e^(-1)

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

Verification of antiderivative is not currently implemented for this CAS.

[In]

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

[Out]

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

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