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

Optimal. Leaf size=29 \[ \text {Int}\left ((f x)^m \left (a+c x^{2 n}\right )^p \left (d+e x^n\right )^q,x\right ) \]

[Out]

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

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Rubi [A]  time = 0.02, antiderivative size = 0, normalized size of antiderivative = 0.00, number of steps used = 0, number of rules used = 0, integrand size = 0, \(\frac {\text {number of rules}}{\text {integrand size}}\) = 0.000, 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*}

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Mathematica [A]  time = 0.20, size = 0, normalized size = 0.00 \[ \int (f x)^m \left (d+e x^n\right )^q \left (a+c x^{2 n}\right )^p \, dx \]

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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fricas [A]  time = 0.91, size = 0, normalized size = 0.00 \[ {\rm integral}\left ({\left (c x^{2 \, n} + a\right )}^{p} {\left (e x^{n} + d\right )}^{q} \left (f x\right )^{m}, x\right ) \]

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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giac [A]  time = 0.00, size = 0, normalized size = 0.00 \[ \int {\left (c x^{2 \, n} + a\right )}^{p} {\left (e x^{n} + d\right )}^{q} \left (f x\right )^{m}\,{d x} \]

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)

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maple [A]  time = 0.43, size = 0, normalized size = 0.00 \[ \int \left (f x \right )^{m} \left (c \,x^{2 n}+a \right )^{p} \left (e \,x^{n}+d \right )^{q}\, dx \]

Verification of antiderivative is not currently implemented for this CAS.

[In]

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

[Out]

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

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maxima [A]  time = 0.00, size = 0, normalized size = 0.00 \[ \int {\left (c x^{2 \, n} + a\right )}^{p} {\left (e x^{n} + d\right )}^{q} \left (f x\right )^{m}\,{d x} \]

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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mupad [A]  time = 0.00, size = -1, normalized size = -0.03 \[ \int {\left (a+c\,x^{2\,n}\right )}^p\,{\left (f\,x\right )}^m\,{\left (d+e\,x^n\right )}^q \,d x \]

Verification of antiderivative is not currently implemented for this CAS.

[In]

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

[Out]

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

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sympy [F(-1)]  time = 0.00, size = 0, normalized size = 0.00 \[ \text {Timed out} \]

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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