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

Optimal. Leaf size=21 \[ \text {Int}\left ((e x)^m \sin \left (a+b (c+d x)^n\right ),x\right ) \]

[Out]

Unintegrable((e*x)^m*sin(a+b*(d*x+c)^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 = {} \[ \int (e x)^m \sin \left (a+b (c+d x)^n\right ) \, dx \]

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 = 6.18, size = 0, normalized size = 0.00 \[ \int (e x)^m \sin \left (a+b (c+d x)^n\right ) \, dx \]

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]

________________________________________________________________________________________

fricas [A]  time = 0.59, size = 0, normalized size = 0.00 \[ {\rm integral}\left (\left (e x\right )^{m} \sin \left ({\left (d x + c\right )}^{n} b + a\right ), x\right ) \]

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)

________________________________________________________________________________________

giac [A]  time = 0.00, size = 0, normalized size = 0.00 \[ \int \left (e x\right )^{m} \sin \left ({\left (d x + c\right )}^{n} b + a\right )\,{d x} \]

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)

________________________________________________________________________________________

maple [A]  time = 0.26, size = 0, normalized size = 0.00 \[ \int \left (e x \right )^{m} \sin \left (a +b \left (d x +c \right )^{n}\right )\, dx \]

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 = 0.00, size = 0, normalized size = 0.00 \[ \int \left (e x\right )^{m} \sin \left ({\left (d x + c\right )}^{n} b + a\right )\,{d x} \]

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)

________________________________________________________________________________________

mupad [A]  time = 0.00, size = -1, normalized size = -0.05 \[ \int \sin \left (a+b\,{\left (c+d\,x\right )}^n\right )\,{\left (e\,x\right )}^m \,d x \]

Verification of antiderivative is not currently implemented for this CAS.

[In]

int(sin(a + b*(c + d*x)^n)*(e*x)^m,x)

[Out]

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

________________________________________________________________________________________

sympy [A]  time = 0.00, size = 0, normalized size = 0.00 \[ \int \left (e x\right )^{m} \sin {\left (a + b \left (c + d x\right )^{n} \right )}\, dx \]

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)

________________________________________________________________________________________