### 3.86 $$\int (f x)^m (d+e x^n)^q (a+c x^{2 n})^p \, dx$$

Optimal. Leaf size=28 $\text{Unintegrable}\left ((f x)^m \left (a+c x^{2 n}\right )^p \left (d+e x^n\right )^q,x\right )$

[Out]

Defer[Int][(f*x)^m*(d + e*x^n)^q*(a + c*x^(2*n))^p, x]

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Rubi [A]  time = 0.0186216, antiderivative size = 0, normalized size of antiderivative = 0., number of steps used = 0, number of rules used = 0, integrand size = 0, $$\frac{\text{number of rules}}{\text{integrand size}}$$ = 0., Rules used = {} $\int (f x)^m \left (d+e x^n\right )^q \left (a+c x^{2 n}\right )^p \, dx$

Veriﬁcation is Not applicable to the result.

[In]

Int[(f*x)^m*(d + e*x^n)^q*(a + c*x^(2*n))^p,x]

[Out]

Defer[Int][(f*x)^m*(d + e*x^n)^q*(a + c*x^(2*n))^p, x]

Rubi steps

\begin{align*} \int (f x)^m \left (d+e x^n\right )^q \left (a+c x^{2 n}\right )^p \, dx &=\int (f x)^m \left (d+e x^n\right )^q \left (a+c x^{2 n}\right )^p \, dx\\ \end{align*}

Mathematica [A]  time = 0.19132, size = 0, normalized size = 0. $\int (f x)^m \left (d+e x^n\right )^q \left (a+c x^{2 n}\right )^p \, dx$

Veriﬁcation is Not applicable to the result.

[In]

Integrate[(f*x)^m*(d + e*x^n)^q*(a + c*x^(2*n))^p,x]

[Out]

Integrate[(f*x)^m*(d + e*x^n)^q*(a + c*x^(2*n))^p, x]

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Maple [A]  time = 0.424, size = 0, normalized size = 0. \begin{align*} \int \left ( fx \right ) ^{m} \left ( d+e{x}^{n} \right ) ^{q} \left ( a+c{x}^{2\,n} \right ) ^{p}\, dx \end{align*}

Veriﬁcation of antiderivative is not currently implemented for this CAS.

[In]

int((f*x)^m*(d+e*x^n)^q*(a+c*x^(2*n))^p,x)

[Out]

int((f*x)^m*(d+e*x^n)^q*(a+c*x^(2*n))^p,x)

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Maxima [A]  time = 0., size = 0, normalized size = 0. \begin{align*} \int{\left (c x^{2 \, n} + a\right )}^{p}{\left (e x^{n} + d\right )}^{q} \left (f x\right )^{m}\,{d x} \end{align*}

Veriﬁcation of antiderivative is not currently implemented for this CAS.

[In]

integrate((f*x)^m*(d+e*x^n)^q*(a+c*x^(2*n))^p,x, algorithm="maxima")

[Out]

integrate((c*x^(2*n) + a)^p*(e*x^n + d)^q*(f*x)^m, x)

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Fricas [A]  time = 0., size = 0, normalized size = 0. \begin{align*}{\rm integral}\left ({\left (c x^{2 \, n} + a\right )}^{p}{\left (e x^{n} + d\right )}^{q} \left (f x\right )^{m}, x\right ) \end{align*}

Veriﬁcation of antiderivative is not currently implemented for this CAS.

[In]

integrate((f*x)^m*(d+e*x^n)^q*(a+c*x^(2*n))^p,x, algorithm="fricas")

[Out]

integral((c*x^(2*n) + a)^p*(e*x^n + d)^q*(f*x)^m, x)

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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((f*x)**m*(d+e*x**n)**q*(a+c*x**(2*n))**p,x)

[Out]

Timed out

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Giac [A]  time = 0., size = 0, normalized size = 0. \begin{align*} \int{\left (c x^{2 \, n} + a\right )}^{p}{\left (e x^{n} + d\right )}^{q} \left (f x\right )^{m}\,{d x} \end{align*}

Veriﬁcation of antiderivative is not currently implemented for this CAS.

[In]

integrate((f*x)^m*(d+e*x^n)^q*(a+c*x^(2*n))^p,x, algorithm="giac")

[Out]

integrate((c*x^(2*n) + a)^p*(e*x^n + d)^q*(f*x)^m, x)