Optimal. Leaf size=32 \[ x^{-m} (e x)^m \text {Int}\left (x^m \left (a+b \text {sech}\left (c+d x^n\right )\right )^p,x\right ) \]
[Out]
________________________________________________________________________________________
Rubi [A] time = 0.06, 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 = {} \[ \int (e x)^m \left (a+b \text {sech}\left (c+d x^n\right )\right )^p \, dx \]
Verification is Not applicable to the result.
[In]
[Out]
Rubi steps
\begin {align*} \int (e x)^m \left (a+b \text {sech}\left (c+d x^n\right )\right )^p \, dx &=\left (x^{-m} (e x)^m\right ) \int x^m \left (a+b \text {sech}\left (c+d x^n\right )\right )^p \, dx\\ \end {align*}
________________________________________________________________________________________
Mathematica [A] time = 18.34, size = 0, normalized size = 0.00 \[ \int (e x)^m \left (a+b \text {sech}\left (c+d x^n\right )\right )^p \, dx \]
Verification is Not applicable to the result.
[In]
[Out]
________________________________________________________________________________________
fricas [A] time = 0.44, size = 0, normalized size = 0.00 \[ {\rm integral}\left (\left (e x\right )^{m} {\left (b \operatorname {sech}\left (d x^{n} + c\right ) + a\right )}^{p}, x\right ) \]
Verification of antiderivative is not currently implemented for this CAS.
[In]
[Out]
________________________________________________________________________________________
giac [A] time = 0.00, size = 0, normalized size = 0.00 \[ \int \left (e x\right )^{m} {\left (b \operatorname {sech}\left (d x^{n} + c\right ) + a\right )}^{p}\,{d x} \]
Verification of antiderivative is not currently implemented for this CAS.
[In]
[Out]
________________________________________________________________________________________
maple [A] time = 0.70, size = 0, normalized size = 0.00 \[ \int \left (e x \right )^{m} \left (a +b \,\mathrm {sech}\left (c +d \,x^{n}\right )\right )^{p}\, dx \]
Verification of antiderivative is not currently implemented for this CAS.
[In]
[Out]
________________________________________________________________________________________
maxima [A] time = 0.00, size = 0, normalized size = 0.00 \[ \int \left (e x\right )^{m} {\left (b \operatorname {sech}\left (d x^{n} + c\right ) + a\right )}^{p}\,{d x} \]
Verification of antiderivative is not currently implemented for this CAS.
[In]
[Out]
________________________________________________________________________________________
mupad [A] time = 0.00, size = -1, normalized size = -0.03 \[ \int {\left (a+\frac {b}{\mathrm {cosh}\left (c+d\,x^n\right )}\right )}^p\,{\left (e\,x\right )}^m \,d x \]
Verification of antiderivative is not currently implemented for this CAS.
[In]
[Out]
________________________________________________________________________________________
sympy [A] time = 0.00, size = 0, normalized size = 0.00 \[ \int \left (e x\right )^{m} \left (a + b \operatorname {sech}{\left (c + d x^{n} \right )}\right )^{p}\, dx \]
Verification of antiderivative is not currently implemented for this CAS.
[In]
[Out]
________________________________________________________________________________________