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

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

[Out]

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

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Rubi [A]  time = 0.0418718, 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 = {} \[ \int (c+d x)^m (b \sin (e+f x))^n \, dx \]

Verification is Not applicable to the result.

[In]

Int[(c + d*x)^m*(b*Sin[e + f*x])^n,x]

[Out]

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

Rubi steps

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

Mathematica [A]  time = 0.721235, size = 0, normalized size = 0. \[ \int (c+d x)^m (b \sin (e+f x))^n \, dx \]

Verification is Not applicable to the result.

[In]

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

[Out]

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

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Maple [A]  time = 0.299, size = 0, normalized size = 0. \begin{align*} \int \left ( dx+c \right ) ^{m} \left ( b\sin \left ( fx+e \right ) \right ) ^{n}\, dx \end{align*}

Verification of antiderivative is not currently implemented for this CAS.

[In]

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

[Out]

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

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

Verification of antiderivative is not currently implemented for this CAS.

[In]

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

[Out]

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

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

Verification of antiderivative is not currently implemented for this CAS.

[In]

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

[Out]

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

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

Verification of antiderivative is not currently implemented for this CAS.

[In]

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

[Out]

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

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

Verification of antiderivative is not currently implemented for this CAS.

[In]

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

[Out]

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