3.1.86 \(\int (f x)^m (d+e x^n)^q (a+c x^{2 n})^p \, dx\) [86]

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

[Out]

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

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Rubi [A]
time = 0.01, 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 = {} \begin {gather*} \int (f x)^m \left (d+e x^n\right )^q \left (a+c x^{2 n}\right )^p \, dx \end {gather*}

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 = 0.18, size = 0, normalized size = 0.00 \begin {gather*} \int (f x)^m \left (d+e x^n\right )^q \left (a+c x^{2 n}\right )^p \, dx \end {gather*}

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 = 0.18, size = 0, normalized size = 0.00 \[\int \left (f x \right )^{m} \left (d +e \,x^{n}\right )^{q} \left (a +c \,x^{2 n}\right )^{p}\, dx\]

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 = 0.00, 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*x)^m*(d+e*x^n)^q*(a+c*x^(2*n))^p,x, algorithm="maxima")

[Out]

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

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Fricas [A]
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((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*(f*x)^m*(x^n*e + d)^q, x)

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Sympy [F(-1)] Timed out
time = 0.00, size = 0, normalized size = 0.00 \begin {gather*} \text {Timed out} \end {gather*}

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 = 0.00, 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((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*(f*x)^m*(x^n*e + d)^q, x)

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

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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