\(\int \frac {x^m}{\text {arccosh}(a x)} \, dx\) [119]

Optimal result

Integrand size = 10, antiderivative size = 10 \[ \int \frac {x^m}{\text {arccosh}(a x)} \, dx=\text {Int}\left (\frac {x^m}{\text {arccosh}(a x)},x\right ) \]

[Out]

Unintegrable(x^m/arccosh(a*x),x)

Rubi [N/A]

Not integrable

Time = 0.01 (sec) , antiderivative size = 10, normalized size of antiderivative = 1.00, number of steps used = 0, number of rules used = 0, \(\frac {\text {number of rules}}{\text {integrand size}}\) = 0.000, Rules used = {} \[ \int \frac {x^m}{\text {arccosh}(a x)} \, dx=\int \frac {x^m}{\text {arccosh}(a x)} \, dx \]

[In]

Int[x^m/ArcCosh[a*x],x]

[Out]

Defer[Int][x^m/ArcCosh[a*x], x]

Rubi steps \begin{align*} \text {integral}& = \int \frac {x^m}{\text {arccosh}(a x)} \, dx \\ \end{align*}

Mathematica [N/A]

Not integrable

Time = 0.68 (sec) , antiderivative size = 12, normalized size of antiderivative = 1.20 \[ \int \frac {x^m}{\text {arccosh}(a x)} \, dx=\int \frac {x^m}{\text {arccosh}(a x)} \, dx \]

[In]

Integrate[x^m/ArcCosh[a*x],x]

[Out]

Integrate[x^m/ArcCosh[a*x], x]

Maple [N/A] (verified)

Not integrable

Time = 0.67 (sec) , antiderivative size = 10, normalized size of antiderivative = 1.00

\[\int \frac {x^{m}}{\operatorname {arccosh}\left (a x \right )}d x\]

[In]

int(x^m/arccosh(a*x),x)

[Out]

int(x^m/arccosh(a*x),x)

Fricas [N/A]

Not integrable

Time = 0.24 (sec) , antiderivative size = 12, normalized size of antiderivative = 1.20 \[ \int \frac {x^m}{\text {arccosh}(a x)} \, dx=\int { \frac {x^{m}}{\operatorname {arcosh}\left (a x\right )} \,d x } \]

[In]

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

[Out]

integral(x^m/arccosh(a*x), x)

Sympy [N/A]

Not integrable

Time = 0.67 (sec) , antiderivative size = 8, normalized size of antiderivative = 0.80 \[ \int \frac {x^m}{\text {arccosh}(a x)} \, dx=\int \frac {x^{m}}{\operatorname {acosh}{\left (a x \right )}}\, dx \]

[In]

integrate(x**m/acosh(a*x),x)

[Out]

Integral(x**m/acosh(a*x), x)

Maxima [N/A]

Not integrable

Time = 0.37 (sec) , antiderivative size = 12, normalized size of antiderivative = 1.20 \[ \int \frac {x^m}{\text {arccosh}(a x)} \, dx=\int { \frac {x^{m}}{\operatorname {arcosh}\left (a x\right )} \,d x } \]

[In]

integrate(x^m/arccosh(a*x),x, algorithm="maxima")

[Out]

integrate(x^m/arccosh(a*x), x)

Giac [N/A]

Not integrable

Time = 0.29 (sec) , antiderivative size = 12, normalized size of antiderivative = 1.20 \[ \int \frac {x^m}{\text {arccosh}(a x)} \, dx=\int { \frac {x^{m}}{\operatorname {arcosh}\left (a x\right )} \,d x } \]

[In]

integrate(x^m/arccosh(a*x),x, algorithm="giac")

[Out]

integrate(x^m/arccosh(a*x), x)

Mupad [N/A]

Not integrable

Time = 2.50 (sec) , antiderivative size = 12, normalized size of antiderivative = 1.20 \[ \int \frac {x^m}{\text {arccosh}(a x)} \, dx=\int \frac {x^m}{\mathrm {acosh}\left (a\,x\right )} \,d x \]

[In]

int(x^m/acosh(a*x),x)

[Out]

int(x^m/acosh(a*x), x)