3.2.85 \(\int \frac {(a+b x)^n (c+d x^3)^3}{x} \, dx\) [185]
Optimal. Leaf size=358 \[ \frac {a^2 d \left (3 b^6 c^2-3 a^3 b^3 c d+a^6 d^2\right ) (a+b x)^{1+n}}{b^9 (1+n)}-\frac {a d \left (6 b^6 c^2-15 a^3 b^3 c d+8 a^6 d^2\right ) (a+b x)^{2+n}}{b^9 (2+n)}+\frac {d \left (3 b^6 c^2-30 a^3 b^3 c d+28 a^6 d^2\right ) (a+b x)^{3+n}}{b^9 (3+n)}+\frac {2 a^2 d^2 \left (15 b^3 c-28 a^3 d\right ) (a+b x)^{4+n}}{b^9 (4+n)}-\frac {5 a d^2 \left (3 b^3 c-14 a^3 d\right ) (a+b x)^{5+n}}{b^9 (5+n)}+\frac {d^2 \left (3 b^3 c-56 a^3 d\right ) (a+b x)^{6+n}}{b^9 (6+n)}+\frac {28 a^2 d^3 (a+b x)^{7+n}}{b^9 (7+n)}-\frac {8 a d^3 (a+b x)^{8+n}}{b^9 (8+n)}+\frac {d^3 (a+b x)^{9+n}}{b^9 (9+n)}-\frac {c^3 (a+b x)^{1+n} \, _2F_1\left (1,1+n;2+n;1+\frac {b x}{a}\right )}{a (1+n)} \]
[Out]
a^2*d*(a^6*d^2-3*a^3*b^3*c*d+3*b^6*c^2)*(b*x+a)^(1+n)/b^9/(1+n)-a*d*(8*a^6*d^2-15*a^3*b^3*c*d+6*b^6*c^2)*(b*x+
a)^(2+n)/b^9/(2+n)+d*(28*a^6*d^2-30*a^3*b^3*c*d+3*b^6*c^2)*(b*x+a)^(3+n)/b^9/(3+n)+2*a^2*d^2*(-28*a^3*d+15*b^3
*c)*(b*x+a)^(4+n)/b^9/(4+n)-5*a*d^2*(-14*a^3*d+3*b^3*c)*(b*x+a)^(5+n)/b^9/(5+n)+d^2*(-56*a^3*d+3*b^3*c)*(b*x+a
)^(6+n)/b^9/(6+n)+28*a^2*d^3*(b*x+a)^(7+n)/b^9/(7+n)-8*a*d^3*(b*x+a)^(8+n)/b^9/(8+n)+d^3*(b*x+a)^(9+n)/b^9/(9+
n)-c^3*(b*x+a)^(1+n)*hypergeom([1, 1+n],[2+n],1+b*x/a)/a/(1+n)
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Rubi [A]
time = 0.15, antiderivative size = 358, normalized size of antiderivative = 1.00, number of steps
used = 3, number of rules used = 2, integrand size = 20, \(\frac {\text {number of rules}}{\text {integrand size}}\) = 0.100, Rules used = {1634, 67}
\begin {gather*} -\frac {5 a d^2 \left (3 b^3 c-14 a^3 d\right ) (a+b x)^{n+5}}{b^9 (n+5)}+\frac {d^2 \left (3 b^3 c-56 a^3 d\right ) (a+b x)^{n+6}}{b^9 (n+6)}+\frac {28 a^2 d^3 (a+b x)^{n+7}}{b^9 (n+7)}-\frac {a d \left (8 a^6 d^2-15 a^3 b^3 c d+6 b^6 c^2\right ) (a+b x)^{n+2}}{b^9 (n+2)}+\frac {d \left (28 a^6 d^2-30 a^3 b^3 c d+3 b^6 c^2\right ) (a+b x)^{n+3}}{b^9 (n+3)}+\frac {2 a^2 d^2 \left (15 b^3 c-28 a^3 d\right ) (a+b x)^{n+4}}{b^9 (n+4)}+\frac {a^2 d \left (a^6 d^2-3 a^3 b^3 c d+3 b^6 c^2\right ) (a+b x)^{n+1}}{b^9 (n+1)}-\frac {8 a d^3 (a+b x)^{n+8}}{b^9 (n+8)}+\frac {d^3 (a+b x)^{n+9}}{b^9 (n+9)}-\frac {c^3 (a+b x)^{n+1} \, _2F_1\left (1,n+1;n+2;\frac {b x}{a}+1\right )}{a (n+1)} \end {gather*}
Antiderivative was successfully verified.
[In]
Int[((a + b*x)^n*(c + d*x^3)^3)/x,x]
[Out]
(a^2*d*(3*b^6*c^2 - 3*a^3*b^3*c*d + a^6*d^2)*(a + b*x)^(1 + n))/(b^9*(1 + n)) - (a*d*(6*b^6*c^2 - 15*a^3*b^3*c
*d + 8*a^6*d^2)*(a + b*x)^(2 + n))/(b^9*(2 + n)) + (d*(3*b^6*c^2 - 30*a^3*b^3*c*d + 28*a^6*d^2)*(a + b*x)^(3 +
n))/(b^9*(3 + n)) + (2*a^2*d^2*(15*b^3*c - 28*a^3*d)*(a + b*x)^(4 + n))/(b^9*(4 + n)) - (5*a*d^2*(3*b^3*c - 1
4*a^3*d)*(a + b*x)^(5 + n))/(b^9*(5 + n)) + (d^2*(3*b^3*c - 56*a^3*d)*(a + b*x)^(6 + n))/(b^9*(6 + n)) + (28*a
^2*d^3*(a + b*x)^(7 + n))/(b^9*(7 + n)) - (8*a*d^3*(a + b*x)^(8 + n))/(b^9*(8 + n)) + (d^3*(a + b*x)^(9 + n))/
(b^9*(9 + n)) - (c^3*(a + b*x)^(1 + n)*Hypergeometric2F1[1, 1 + n, 2 + n, 1 + (b*x)/a])/(a*(1 + n))
Rule 67
Int[((b_.)*(x_))^(m_)*((c_) + (d_.)*(x_))^(n_), x_Symbol] :> Simp[((c + d*x)^(n + 1)/(d*(n + 1)*(-d/(b*c))^m))
*Hypergeometric2F1[-m, n + 1, n + 2, 1 + d*(x/c)], x] /; FreeQ[{b, c, d, m, n}, x] && !IntegerQ[n] && (Intege
rQ[m] || GtQ[-d/(b*c), 0])
Rule 1634
Int[(Px_)*((a_.) + (b_.)*(x_))^(m_.)*((c_.) + (d_.)*(x_))^(n_.), x_Symbol] :> Int[ExpandIntegrand[Px*(a + b*x)
^m*(c + d*x)^n, x], x] /; FreeQ[{a, b, c, d, m, n}, x] && PolyQ[Px, x] && (IntegersQ[m, n] || IGtQ[m, -2]) &&
GtQ[Expon[Px, x], 2]
Rubi steps
\begin {align*} \int \frac {(a+b x)^n \left (c+d x^3\right )^3}{x} \, dx &=\int \left (\frac {a^2 d \left (3 b^6 c^2-3 a^3 b^3 c d+a^6 d^2\right ) (a+b x)^n}{b^8}+\frac {c^3 (a+b x)^n}{x}-\frac {a d \left (6 b^6 c^2-15 a^3 b^3 c d+8 a^6 d^2\right ) (a+b x)^{1+n}}{b^8}+\frac {d \left (3 b^6 c^2-30 a^3 b^3 c d+28 a^6 d^2\right ) (a+b x)^{2+n}}{b^8}-\frac {2 a^2 d^2 \left (-15 b^3 c+28 a^3 d\right ) (a+b x)^{3+n}}{b^8}+\frac {5 a d^2 \left (-3 b^3 c+14 a^3 d\right ) (a+b x)^{4+n}}{b^8}+\frac {d^2 \left (3 b^3 c-56 a^3 d\right ) (a+b x)^{5+n}}{b^8}+\frac {28 a^2 d^3 (a+b x)^{6+n}}{b^8}-\frac {8 a d^3 (a+b x)^{7+n}}{b^8}+\frac {d^3 (a+b x)^{8+n}}{b^8}\right ) \, dx\\ &=\frac {a^2 d \left (3 b^6 c^2-3 a^3 b^3 c d+a^6 d^2\right ) (a+b x)^{1+n}}{b^9 (1+n)}-\frac {a d \left (6 b^6 c^2-15 a^3 b^3 c d+8 a^6 d^2\right ) (a+b x)^{2+n}}{b^9 (2+n)}+\frac {d \left (3 b^6 c^2-30 a^3 b^3 c d+28 a^6 d^2\right ) (a+b x)^{3+n}}{b^9 (3+n)}+\frac {2 a^2 d^2 \left (15 b^3 c-28 a^3 d\right ) (a+b x)^{4+n}}{b^9 (4+n)}-\frac {5 a d^2 \left (3 b^3 c-14 a^3 d\right ) (a+b x)^{5+n}}{b^9 (5+n)}+\frac {d^2 \left (3 b^3 c-56 a^3 d\right ) (a+b x)^{6+n}}{b^9 (6+n)}+\frac {28 a^2 d^3 (a+b x)^{7+n}}{b^9 (7+n)}-\frac {8 a d^3 (a+b x)^{8+n}}{b^9 (8+n)}+\frac {d^3 (a+b x)^{9+n}}{b^9 (9+n)}+c^3 \int \frac {(a+b x)^n}{x} \, dx\\ &=\frac {a^2 d \left (3 b^6 c^2-3 a^3 b^3 c d+a^6 d^2\right ) (a+b x)^{1+n}}{b^9 (1+n)}-\frac {a d \left (6 b^6 c^2-15 a^3 b^3 c d+8 a^6 d^2\right ) (a+b x)^{2+n}}{b^9 (2+n)}+\frac {d \left (3 b^6 c^2-30 a^3 b^3 c d+28 a^6 d^2\right ) (a+b x)^{3+n}}{b^9 (3+n)}+\frac {2 a^2 d^2 \left (15 b^3 c-28 a^3 d\right ) (a+b x)^{4+n}}{b^9 (4+n)}-\frac {5 a d^2 \left (3 b^3 c-14 a^3 d\right ) (a+b x)^{5+n}}{b^9 (5+n)}+\frac {d^2 \left (3 b^3 c-56 a^3 d\right ) (a+b x)^{6+n}}{b^9 (6+n)}+\frac {28 a^2 d^3 (a+b x)^{7+n}}{b^9 (7+n)}-\frac {8 a d^3 (a+b x)^{8+n}}{b^9 (8+n)}+\frac {d^3 (a+b x)^{9+n}}{b^9 (9+n)}-\frac {c^3 (a+b x)^{1+n} \, _2F_1\left (1,1+n;2+n;1+\frac {b x}{a}\right )}{a (1+n)}\\ \end {align*}
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Mathematica [A]
time = 0.30, size = 332, normalized size = 0.93 \begin {gather*} (a+b x)^{1+n} \left (\frac {a^2 d \left (3 b^6 c^2-3 a^3 b^3 c d+a^6 d^2\right )}{b^9 (1+n)}-\frac {a d \left (6 b^6 c^2-15 a^3 b^3 c d+8 a^6 d^2\right ) (a+b x)}{b^9 (2+n)}+\frac {d \left (3 b^6 c^2-30 a^3 b^3 c d+28 a^6 d^2\right ) (a+b x)^2}{b^9 (3+n)}+\frac {2 a^2 d^2 \left (15 b^3 c-28 a^3 d\right ) (a+b x)^3}{b^9 (4+n)}+\frac {5 a d^2 \left (-3 b^3 c+14 a^3 d\right ) (a+b x)^4}{b^9 (5+n)}+\frac {d^2 \left (3 b^3 c-56 a^3 d\right ) (a+b x)^5}{b^9 (6+n)}+\frac {28 a^2 d^3 (a+b x)^6}{b^9 (7+n)}-\frac {8 a d^3 (a+b x)^7}{b^9 (8+n)}+\frac {d^3 (a+b x)^8}{b^9 (9+n)}-\frac {c^3 \, _2F_1\left (1,1+n;2+n;\frac {a+b x}{a}\right )}{a+a n}\right ) \end {gather*}
Antiderivative was successfully verified.
[In]
Integrate[((a + b*x)^n*(c + d*x^3)^3)/x,x]
[Out]
(a + b*x)^(1 + n)*((a^2*d*(3*b^6*c^2 - 3*a^3*b^3*c*d + a^6*d^2))/(b^9*(1 + n)) - (a*d*(6*b^6*c^2 - 15*a^3*b^3*
c*d + 8*a^6*d^2)*(a + b*x))/(b^9*(2 + n)) + (d*(3*b^6*c^2 - 30*a^3*b^3*c*d + 28*a^6*d^2)*(a + b*x)^2)/(b^9*(3
+ n)) + (2*a^2*d^2*(15*b^3*c - 28*a^3*d)*(a + b*x)^3)/(b^9*(4 + n)) + (5*a*d^2*(-3*b^3*c + 14*a^3*d)*(a + b*x)
^4)/(b^9*(5 + n)) + (d^2*(3*b^3*c - 56*a^3*d)*(a + b*x)^5)/(b^9*(6 + n)) + (28*a^2*d^3*(a + b*x)^6)/(b^9*(7 +
n)) - (8*a*d^3*(a + b*x)^7)/(b^9*(8 + n)) + (d^3*(a + b*x)^8)/(b^9*(9 + n)) - (c^3*Hypergeometric2F1[1, 1 + n,
2 + n, (a + b*x)/a])/(a + a*n))
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Maple [F]
time = 0.04, size = 0, normalized size = 0.00 \[\int \frac {\left (b x +a \right )^{n} \left (d \,x^{3}+c \right )^{3}}{x}\, dx\]
Verification of antiderivative is not currently implemented for this CAS.
[In]
int((b*x+a)^n*(d*x^3+c)^3/x,x)
[Out]
int((b*x+a)^n*(d*x^3+c)^3/x,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((b*x+a)^n*(d*x^3+c)^3/x,x, algorithm="maxima")
[Out]
integrate((d*x^3 + c)^3*(b*x + a)^n/x, x)
________________________________________________________________________________________
Fricas [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((b*x+a)^n*(d*x^3+c)^3/x,x, algorithm="fricas")
[Out]
integral((d^3*x^9 + 3*c*d^2*x^6 + 3*c^2*d*x^3 + c^3)*(b*x + a)^n/x, x)
________________________________________________________________________________________
Sympy [B] Leaf count of result is larger than twice the leaf count of optimal. 12492 vs.
\(2 (338) = 676\).
time = 14.40, size = 17258, normalized size = 48.21 \begin {gather*} \text {Too large to display} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
[In]
integrate((b*x+a)**n*(d*x**3+c)**3/x,x)
[Out]
-b**n*c**3*n*(a/b + x)**n*lerchphi(1 + b*x/a, 1, n + 1)*gamma(n + 1)/gamma(n + 2) - b**n*c**3*(a/b + x)**n*ler
chphi(1 + b*x/a, 1, n + 1)*gamma(n + 1)/gamma(n + 2) + 3*c**2*d*Piecewise((a**n*x**3/3, Eq(b, 0)), (2*a**2*log
(a/b + x)/(2*a**2*b**3 + 4*a*b**4*x + 2*b**5*x**2) + 3*a**2/(2*a**2*b**3 + 4*a*b**4*x + 2*b**5*x**2) + 4*a*b*x
*log(a/b + x)/(2*a**2*b**3 + 4*a*b**4*x + 2*b**5*x**2) + 4*a*b*x/(2*a**2*b**3 + 4*a*b**4*x + 2*b**5*x**2) + 2*
b**2*x**2*log(a/b + x)/(2*a**2*b**3 + 4*a*b**4*x + 2*b**5*x**2), Eq(n, -3)), (-2*a**2*log(a/b + x)/(a*b**3 + b
**4*x) - 2*a**2/(a*b**3 + b**4*x) - 2*a*b*x*log(a/b + x)/(a*b**3 + b**4*x) + b**2*x**2/(a*b**3 + b**4*x), Eq(n
, -2)), (a**2*log(a/b + x)/b**3 - a*x/b**2 + x**2/(2*b), Eq(n, -1)), (2*a**3*(a + b*x)**n/(b**3*n**3 + 6*b**3*
n**2 + 11*b**3*n + 6*b**3) - 2*a**2*b*n*x*(a + b*x)**n/(b**3*n**3 + 6*b**3*n**2 + 11*b**3*n + 6*b**3) + a*b**2
*n**2*x**2*(a + b*x)**n/(b**3*n**3 + 6*b**3*n**2 + 11*b**3*n + 6*b**3) + a*b**2*n*x**2*(a + b*x)**n/(b**3*n**3
+ 6*b**3*n**2 + 11*b**3*n + 6*b**3) + b**3*n**2*x**3*(a + b*x)**n/(b**3*n**3 + 6*b**3*n**2 + 11*b**3*n + 6*b*
*3) + 3*b**3*n*x**3*(a + b*x)**n/(b**3*n**3 + 6*b**3*n**2 + 11*b**3*n + 6*b**3) + 2*b**3*x**3*(a + b*x)**n/(b*
*3*n**3 + 6*b**3*n**2 + 11*b**3*n + 6*b**3), True)) + 3*c*d**2*Piecewise((a**n*x**6/6, Eq(b, 0)), (60*a**5*log
(a/b + x)/(60*a**5*b**6 + 300*a**4*b**7*x + 600*a**3*b**8*x**2 + 600*a**2*b**9*x**3 + 300*a*b**10*x**4 + 60*b*
*11*x**5) + 137*a**5/(60*a**5*b**6 + 300*a**4*b**7*x + 600*a**3*b**8*x**2 + 600*a**2*b**9*x**3 + 300*a*b**10*x
**4 + 60*b**11*x**5) + 300*a**4*b*x*log(a/b + x)/(60*a**5*b**6 + 300*a**4*b**7*x + 600*a**3*b**8*x**2 + 600*a*
*2*b**9*x**3 + 300*a*b**10*x**4 + 60*b**11*x**5) + 625*a**4*b*x/(60*a**5*b**6 + 300*a**4*b**7*x + 600*a**3*b**
8*x**2 + 600*a**2*b**9*x**3 + 300*a*b**10*x**4 + 60*b**11*x**5) + 600*a**3*b**2*x**2*log(a/b + x)/(60*a**5*b**
6 + 300*a**4*b**7*x + 600*a**3*b**8*x**2 + 600*a**2*b**9*x**3 + 300*a*b**10*x**4 + 60*b**11*x**5) + 1100*a**3*
b**2*x**2/(60*a**5*b**6 + 300*a**4*b**7*x + 600*a**3*b**8*x**2 + 600*a**2*b**9*x**3 + 300*a*b**10*x**4 + 60*b*
*11*x**5) + 600*a**2*b**3*x**3*log(a/b + x)/(60*a**5*b**6 + 300*a**4*b**7*x + 600*a**3*b**8*x**2 + 600*a**2*b*
*9*x**3 + 300*a*b**10*x**4 + 60*b**11*x**5) + 900*a**2*b**3*x**3/(60*a**5*b**6 + 300*a**4*b**7*x + 600*a**3*b*
*8*x**2 + 600*a**2*b**9*x**3 + 300*a*b**10*x**4 + 60*b**11*x**5) + 300*a*b**4*x**4*log(a/b + x)/(60*a**5*b**6
+ 300*a**4*b**7*x + 600*a**3*b**8*x**2 + 600*a**2*b**9*x**3 + 300*a*b**10*x**4 + 60*b**11*x**5) + 300*a*b**4*x
**4/(60*a**5*b**6 + 300*a**4*b**7*x + 600*a**3*b**8*x**2 + 600*a**2*b**9*x**3 + 300*a*b**10*x**4 + 60*b**11*x*
*5) + 60*b**5*x**5*log(a/b + x)/(60*a**5*b**6 + 300*a**4*b**7*x + 600*a**3*b**8*x**2 + 600*a**2*b**9*x**3 + 30
0*a*b**10*x**4 + 60*b**11*x**5), Eq(n, -6)), (-60*a**5*log(a/b + x)/(12*a**4*b**6 + 48*a**3*b**7*x + 72*a**2*b
**8*x**2 + 48*a*b**9*x**3 + 12*b**10*x**4) - 125*a**5/(12*a**4*b**6 + 48*a**3*b**7*x + 72*a**2*b**8*x**2 + 48*
a*b**9*x**3 + 12*b**10*x**4) - 240*a**4*b*x*log(a/b + x)/(12*a**4*b**6 + 48*a**3*b**7*x + 72*a**2*b**8*x**2 +
48*a*b**9*x**3 + 12*b**10*x**4) - 440*a**4*b*x/(12*a**4*b**6 + 48*a**3*b**7*x + 72*a**2*b**8*x**2 + 48*a*b**9*
x**3 + 12*b**10*x**4) - 360*a**3*b**2*x**2*log(a/b + x)/(12*a**4*b**6 + 48*a**3*b**7*x + 72*a**2*b**8*x**2 + 4
8*a*b**9*x**3 + 12*b**10*x**4) - 540*a**3*b**2*x**2/(12*a**4*b**6 + 48*a**3*b**7*x + 72*a**2*b**8*x**2 + 48*a*
b**9*x**3 + 12*b**10*x**4) - 240*a**2*b**3*x**3*log(a/b + x)/(12*a**4*b**6 + 48*a**3*b**7*x + 72*a**2*b**8*x**
2 + 48*a*b**9*x**3 + 12*b**10*x**4) - 240*a**2*b**3*x**3/(12*a**4*b**6 + 48*a**3*b**7*x + 72*a**2*b**8*x**2 +
48*a*b**9*x**3 + 12*b**10*x**4) - 60*a*b**4*x**4*log(a/b + x)/(12*a**4*b**6 + 48*a**3*b**7*x + 72*a**2*b**8*x*
*2 + 48*a*b**9*x**3 + 12*b**10*x**4) + 12*b**5*x**5/(12*a**4*b**6 + 48*a**3*b**7*x + 72*a**2*b**8*x**2 + 48*a*
b**9*x**3 + 12*b**10*x**4), Eq(n, -5)), (60*a**5*log(a/b + x)/(6*a**3*b**6 + 18*a**2*b**7*x + 18*a*b**8*x**2 +
6*b**9*x**3) + 110*a**5/(6*a**3*b**6 + 18*a**2*b**7*x + 18*a*b**8*x**2 + 6*b**9*x**3) + 180*a**4*b*x*log(a/b
+ x)/(6*a**3*b**6 + 18*a**2*b**7*x + 18*a*b**8*x**2 + 6*b**9*x**3) + 270*a**4*b*x/(6*a**3*b**6 + 18*a**2*b**7*
x + 18*a*b**8*x**2 + 6*b**9*x**3) + 180*a**3*b**2*x**2*log(a/b + x)/(6*a**3*b**6 + 18*a**2*b**7*x + 18*a*b**8*
x**2 + 6*b**9*x**3) + 180*a**3*b**2*x**2/(6*a**3*b**6 + 18*a**2*b**7*x + 18*a*b**8*x**2 + 6*b**9*x**3) + 60*a*
*2*b**3*x**3*log(a/b + x)/(6*a**3*b**6 + 18*a**2*b**7*x + 18*a*b**8*x**2 + 6*b**9*x**3) - 15*a*b**4*x**4/(6*a*
*3*b**6 + 18*a**2*b**7*x + 18*a*b**8*x**2 + 6*b**9*x**3) + 3*b**5*x**5/(6*a**3*b**6 + 18*a**2*b**7*x + 18*a*b*
*8*x**2 + 6*b**9*x**3), Eq(n, -4)), (-60*a**5*log(a/b + x)/(6*a**2*b**6 + 12*a*b**7*x + 6*b**8*x**2) - 90*a**5
/(6*a**2*b**6 + 12*a*b**7*x + 6*b**8*x**2) - 120*a**4*b*x*log(a/b + x)/(6*a**2*b**6 + 12*a*b**7*x + 6*b**8*x**
2) - 120*a**4*b*x/(6*a**2*b**6 + 12*a*b**7*x + 6*b**8*x**2) - 60*a**3*b**2*x**2*log(a/b + x)/(6*a**2*b**6 + 12
*a*b**7*x + 6*b**8*x**2) + 20*a**2*b**3*x**3/(6...
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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((b*x+a)^n*(d*x^3+c)^3/x,x, algorithm="giac")
[Out]
integrate((d*x^3 + c)^3*(b*x + a)^n/x, x)
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Mupad [F]
time = 0.00, size = -1, normalized size = -0.00 \begin {gather*} \int \frac {{\left (d\,x^3+c\right )}^3\,{\left (a+b\,x\right )}^n}{x} \,d x \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
[In]
int(((c + d*x^3)^3*(a + b*x)^n)/x,x)
[Out]
int(((c + d*x^3)^3*(a + b*x)^n)/x, x)
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