3.259 \(\int (e x)^m \sin (a+b (c+d x)^n) \, dx\)

Optimal. Leaf size=20 \[ \text{Unintegrable}\left ((e x)^m \sin \left (a+b (c+d x)^n\right ),x\right ) \]

[Out]

Unintegrable[(e*x)^m*Sin[a + b*(c + d*x)^n], x]

________________________________________________________________________________________

Rubi [A]  time = 0.009114, antiderivative size = 0, normalized size of antiderivative = 0., number of steps used = 0, number of rules used = 0, integrand size = 0, \(\frac{\text{number of rules}}{\text{integrand size}}\) = 0., Rules used = {} \[ \int (e x)^m \sin \left (a+b (c+d x)^n\right ) \, dx \]

Verification is Not applicable to the result.

[In]

Int[(e*x)^m*Sin[a + b*(c + d*x)^n],x]

[Out]

Defer[Int][(e*x)^m*Sin[a + b*(c + d*x)^n], x]

Rubi steps

\begin{align*} \int (e x)^m \sin \left (a+b (c+d x)^n\right ) \, dx &=\int (e x)^m \sin \left (a+b (c+d x)^n\right ) \, dx\\ \end{align*}

Mathematica [A]  time = 6.09264, size = 0, normalized size = 0. \[ \int (e x)^m \sin \left (a+b (c+d x)^n\right ) \, dx \]

Verification is Not applicable to the result.

[In]

Integrate[(e*x)^m*Sin[a + b*(c + d*x)^n],x]

[Out]

Integrate[(e*x)^m*Sin[a + b*(c + d*x)^n], x]

________________________________________________________________________________________

Maple [A]  time = 0.187, size = 0, normalized size = 0. \begin{align*} \int \left ( ex \right ) ^{m}\sin \left ( a+b \left ( dx+c \right ) ^{n} \right ) \, dx \end{align*}

Verification of antiderivative is not currently implemented for this CAS.

[In]

int((e*x)^m*sin(a+b*(d*x+c)^n),x)

[Out]

int((e*x)^m*sin(a+b*(d*x+c)^n),x)

________________________________________________________________________________________

Maxima [A]  time = 0., size = 0, normalized size = 0. \begin{align*} \int \left (e x\right )^{m} \sin \left ({\left (d x + c\right )}^{n} b + a\right )\,{d x} \end{align*}

Verification of antiderivative is not currently implemented for this CAS.

[In]

integrate((e*x)^m*sin(a+b*(d*x+c)^n),x, algorithm="maxima")

[Out]

integrate((e*x)^m*sin((d*x + c)^n*b + a), x)

________________________________________________________________________________________

Fricas [A]  time = 0., size = 0, normalized size = 0. \begin{align*}{\rm integral}\left (\left (e x\right )^{m} \sin \left ({\left (d x + c\right )}^{n} b + a\right ), x\right ) \end{align*}

Verification of antiderivative is not currently implemented for this CAS.

[In]

integrate((e*x)^m*sin(a+b*(d*x+c)^n),x, algorithm="fricas")

[Out]

integral((e*x)^m*sin((d*x + c)^n*b + a), x)

________________________________________________________________________________________

Sympy [A]  time = 0., size = 0, normalized size = 0. \begin{align*} \int \left (e x\right )^{m} \sin{\left (a + b \left (c + d x\right )^{n} \right )}\, dx \end{align*}

Verification of antiderivative is not currently implemented for this CAS.

[In]

integrate((e*x)**m*sin(a+b*(d*x+c)**n),x)

[Out]

Integral((e*x)**m*sin(a + b*(c + d*x)**n), x)

________________________________________________________________________________________

Giac [A]  time = 0., size = 0, normalized size = 0. \begin{align*} \int \left (e x\right )^{m} \sin \left ({\left (d x + c\right )}^{n} b + a\right )\,{d x} \end{align*}

Verification of antiderivative is not currently implemented for this CAS.

[In]

integrate((e*x)^m*sin(a+b*(d*x+c)^n),x, algorithm="giac")

[Out]

integrate((e*x)^m*sin((d*x + c)^n*b + a), x)