3.2.26 \(\int (d x)^m \cosh ^{-1}(a x)^n \, dx\) [126]

Optimal. Leaf size=15 \[ \text {Int}\left ((d x)^m \cosh ^{-1}(a x)^n,x\right ) \]

[Out]

Unintegrable((d*x)^m*arccosh(a*x)^n,x)

________________________________________________________________________________________

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 (d x)^m \cosh ^{-1}(a x)^n \, dx \end {gather*}

Verification is not applicable to the result.

[In]

Int[(d*x)^m*ArcCosh[a*x]^n,x]

[Out]

Defer[Int][(d*x)^m*ArcCosh[a*x]^n, x]

Rubi steps

\begin {align*} \int (d x)^m \cosh ^{-1}(a x)^n \, dx &=\int (d x)^m \cosh ^{-1}(a x)^n \, dx\\ \end {align*}

________________________________________________________________________________________

Mathematica [A]
time = 1.43, size = 0, normalized size = 0.00 \begin {gather*} \int (d x)^m \cosh ^{-1}(a x)^n \, dx \end {gather*}

Verification is not applicable to the result.

[In]

Integrate[(d*x)^m*ArcCosh[a*x]^n,x]

[Out]

Integrate[(d*x)^m*ArcCosh[a*x]^n, x]

________________________________________________________________________________________

Maple [A]
time = 0.66, size = 0, normalized size = 0.00 \[\int \left (d x \right )^{m} \mathrm {arccosh}\left (a x \right )^{n}\, dx\]

Verification of antiderivative is not currently implemented for this CAS.

[In]

int((d*x)^m*arccosh(a*x)^n,x)

[Out]

int((d*x)^m*arccosh(a*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((d*x)^m*arccosh(a*x)^n,x, algorithm="maxima")

[Out]

integrate((d*x)^m*arccosh(a*x)^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((d*x)^m*arccosh(a*x)^n,x, algorithm="fricas")

[Out]

integral((d*x)^m*arccosh(a*x)^n, x)

________________________________________________________________________________________

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

Verification of antiderivative is not currently implemented for this CAS.

[In]

integrate((d*x)**m*acosh(a*x)**n,x)

[Out]

Integral((d*x)**m*acosh(a*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((d*x)^m*arccosh(a*x)^n,x, algorithm="giac")

[Out]

Timed out

________________________________________________________________________________________

Mupad [A]
time = 0.00, size = -1, normalized size = -0.07 \begin {gather*} \int {\mathrm {acosh}\left (a\,x\right )}^n\,{\left (d\,x\right )}^m \,d x \end {gather*}

Verification of antiderivative is not currently implemented for this CAS.

[In]

int(acosh(a*x)^n*(d*x)^m,x)

[Out]

int(acosh(a*x)^n*(d*x)^m, x)

________________________________________________________________________________________