3.5.54 \(\int (f x)^m (a+b \cosh ^{-1}(c x))^n \, dx\) [454]

Optimal. Leaf size=19 \[ \text {Int}\left ((f x)^m \left (a+b \cosh ^{-1}(c x)\right )^n,x\right ) \]

[Out]

Unintegrable((f*x)^m*(a+b*arccosh(c*x))^n,x)

________________________________________________________________________________________

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 = {} \begin {gather*} \int (f x)^m \left (a+b \cosh ^{-1}(c x)\right )^n \, dx \end {gather*}

Verification is not applicable to the result.

[In]

Int[(f*x)^m*(a + b*ArcCosh[c*x])^n,x]

[Out]

Defer[Int][(f*x)^m*(a + b*ArcCosh[c*x])^n, x]

Rubi steps

\begin {align*} \int (f x)^m \left (a+b \cosh ^{-1}(c x)\right )^n \, dx &=\int (f x)^m \left (a+b \cosh ^{-1}(c x)\right )^n \, dx\\ \end {align*}

________________________________________________________________________________________

Mathematica [A]
time = 0.03, size = 0, normalized size = 0.00 \begin {gather*} \int (f x)^m \left (a+b \cosh ^{-1}(c x)\right )^n \, dx \end {gather*}

Verification is not applicable to the result.

[In]

Integrate[(f*x)^m*(a + b*ArcCosh[c*x])^n,x]

[Out]

Integrate[(f*x)^m*(a + b*ArcCosh[c*x])^n, x]

________________________________________________________________________________________

Maple [A]
time = 180.00, size = 0, normalized size = 0.00 \[\int \left (f x \right )^{m} \left (a +b \,\mathrm {arccosh}\left (c x \right )\right )^{n}\, dx\]

Verification of antiderivative is not currently implemented for this CAS.

[In]

int((f*x)^m*(a+b*arccosh(c*x))^n,x)

[Out]

int((f*x)^m*(a+b*arccosh(c*x))^n,x)

________________________________________________________________________________________

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*(a+b*arccosh(c*x))^n,x, algorithm="maxima")

[Out]

integrate((f*x)^m*(b*arccosh(c*x) + a)^n, x)

________________________________________________________________________________________

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*(a+b*arccosh(c*x))^n,x, algorithm="fricas")

[Out]

integral((f*x)^m*(b*arccosh(c*x) + a)^n, x)

________________________________________________________________________________________

Sympy [A]
time = 0.00, size = 0, normalized size = 0.00 \begin {gather*} \int \left (f x\right )^{m} \left (a + b \operatorname {acosh}{\left (c x \right )}\right )^{n}\, dx \end {gather*}

Verification of antiderivative is not currently implemented for this CAS.

[In]

integrate((f*x)**m*(a+b*acosh(c*x))**n,x)

[Out]

Integral((f*x)**m*(a + b*acosh(c*x))**n, x)

________________________________________________________________________________________

Giac [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*(a+b*arccosh(c*x))^n,x, algorithm="giac")

[Out]

Timed out

________________________________________________________________________________________

Mupad [A]
time = 0.00, size = -1, normalized size = -0.05 \begin {gather*} \int {\left (a+b\,\mathrm {acosh}\left (c\,x\right )\right )}^n\,{\left (f\,x\right )}^m \,d x \end {gather*}

Verification of antiderivative is not currently implemented for this CAS.

[In]

int((a + b*acosh(c*x))^n*(f*x)^m,x)

[Out]

int((a + b*acosh(c*x))^n*(f*x)^m, x)

________________________________________________________________________________________