Optimal. Leaf size=28 \[ b \text {Int}\left (\frac {\sin \left (c+d (f+g x)^n\right )}{x^2},x\right )-\frac {a}{x} \]
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Rubi [A] time = 0.02, 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 = {} \[ \int \frac {a+b \sin \left (c+d (f+g x)^n\right )}{x^2} \, dx \]
Verification is Not applicable to the result.
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Rubi steps
\begin {align*} \int \frac {a+b \sin \left (c+d (f+g x)^n\right )}{x^2} \, dx &=\int \left (\frac {a}{x^2}+\frac {b \sin \left (c+d (f+g x)^n\right )}{x^2}\right ) \, dx\\ &=-\frac {a}{x}+b \int \frac {\sin \left (c+d (f+g x)^n\right )}{x^2} \, dx\\ \end {align*}
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Mathematica [A] time = 2.89, size = 0, normalized size = 0.00 \[ \int \frac {a+b \sin \left (c+d (f+g x)^n\right )}{x^2} \, dx \]
Verification is Not applicable to the result.
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fricas [A] time = 0.70, size = 0, normalized size = 0.00 \[ {\rm integral}\left (\frac {b \sin \left ({\left (g x + f\right )}^{n} d + c\right ) + a}{x^{2}}, x\right ) \]
Verification of antiderivative is not currently implemented for this CAS.
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giac [A] time = 0.00, size = 0, normalized size = 0.00 \[ \int \frac {b \sin \left ({\left (g x + f\right )}^{n} d + c\right ) + a}{x^{2}}\,{d x} \]
Verification of antiderivative is not currently implemented for this CAS.
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maple [A] time = 0.18, size = 0, normalized size = 0.00 \[ \int \frac {a +b \sin \left (c +d \left (g x +f \right )^{n}\right )}{x^{2}}\, dx \]
Verification of antiderivative is not currently implemented for this CAS.
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maxima [A] time = 0.00, size = 0, normalized size = 0.00 \[ b \int \frac {\sin \left ({\left (g x + f\right )}^{n} d + c\right )}{x^{2}}\,{d x} - \frac {a}{x} \]
Verification of antiderivative is not currently implemented for this CAS.
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mupad [A] time = 0.00, size = -1, normalized size = -0.04 \[ \int \frac {a+b\,\sin \left (c+d\,{\left (f+g\,x\right )}^n\right )}{x^2} \,d x \]
Verification of antiderivative is not currently implemented for this CAS.
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sympy [A] time = 0.00, size = 0, normalized size = 0.00 \[ \int \frac {a + b \sin {\left (c + d \left (f + g x\right )^{n} \right )}}{x^{2}}\, dx \]
Verification of antiderivative is not currently implemented for this CAS.
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