3.265 \(\int \frac{\sin (a+b (c+d x)^n)}{x^2} \, dx\)

Optimal. Leaf size=18 \[ \text{Unintegrable}\left (\frac{\sin \left (a+b (c+d x)^n\right )}{x^2},x\right ) \]

[Out]

Unintegrable[Sin[a + b*(c + d*x)^n]/x^2, x]

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Rubi [A]  time = 0.009085, 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 = {} \[ \int \frac{\sin \left (a+b (c+d x)^n\right )}{x^2} \, dx \]

Verification is Not applicable to the result.

[In]

Int[Sin[a + b*(c + d*x)^n]/x^2,x]

[Out]

Defer[Int][Sin[a + b*(c + d*x)^n]/x^2, x]

Rubi steps

\begin{align*} \int \frac{\sin \left (a+b (c+d x)^n\right )}{x^2} \, dx &=\int \frac{\sin \left (a+b (c+d x)^n\right )}{x^2} \, dx\\ \end{align*}

Mathematica [A]  time = 1.60642, size = 0, normalized size = 0. \[ \int \frac{\sin \left (a+b (c+d x)^n\right )}{x^2} \, dx \]

Verification is Not applicable to the result.

[In]

Integrate[Sin[a + b*(c + d*x)^n]/x^2,x]

[Out]

Integrate[Sin[a + b*(c + d*x)^n]/x^2, x]

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Maple [A]  time = 0.09, size = 0, normalized size = 0. \begin{align*} \int{\frac{\sin \left ( a+b \left ( dx+c \right ) ^{n} \right ) }{{x}^{2}}}\, dx \end{align*}

Verification of antiderivative is not currently implemented for this CAS.

[In]

int(sin(a+b*(d*x+c)^n)/x^2,x)

[Out]

int(sin(a+b*(d*x+c)^n)/x^2,x)

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Maxima [A]  time = 0., size = 0, normalized size = 0. \begin{align*} \int \frac{\sin \left ({\left (d x + c\right )}^{n} b + a\right )}{x^{2}}\,{d x} \end{align*}

Verification of antiderivative is not currently implemented for this CAS.

[In]

integrate(sin(a+b*(d*x+c)^n)/x^2,x, algorithm="maxima")

[Out]

integrate(sin((d*x + c)^n*b + a)/x^2, x)

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Fricas [A]  time = 0., size = 0, normalized size = 0. \begin{align*}{\rm integral}\left (\frac{\sin \left ({\left (d x + c\right )}^{n} b + a\right )}{x^{2}}, x\right ) \end{align*}

Verification of antiderivative is not currently implemented for this CAS.

[In]

integrate(sin(a+b*(d*x+c)^n)/x^2,x, algorithm="fricas")

[Out]

integral(sin((d*x + c)^n*b + a)/x^2, x)

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Sympy [A]  time = 0., size = 0, normalized size = 0. \begin{align*} \int \frac{\sin{\left (a + b \left (c + d x\right )^{n} \right )}}{x^{2}}\, dx \end{align*}

Verification of antiderivative is not currently implemented for this CAS.

[In]

integrate(sin(a+b*(d*x+c)**n)/x**2,x)

[Out]

Integral(sin(a + b*(c + d*x)**n)/x**2, x)

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Giac [A]  time = 0., size = 0, normalized size = 0. \begin{align*} \int \frac{\sin \left ({\left (d x + c\right )}^{n} b + a\right )}{x^{2}}\,{d x} \end{align*}

Verification of antiderivative is not currently implemented for this CAS.

[In]

integrate(sin(a+b*(d*x+c)^n)/x^2,x, algorithm="giac")

[Out]

integrate(sin((d*x + c)^n*b + a)/x^2, x)