Optimal. Leaf size=11 \[ -\frac {\cot (a+b x)}{b} \]
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Rubi [A] time = 0.01, antiderivative size = 11, normalized size of antiderivative = 1.00, number of steps used = 2, number of rules used = 2, integrand size = 8, \(\frac {\text {number of rules}}{\text {integrand size}}\) = 0.250, Rules used = {3767, 8} \[ -\frac {\cot (a+b x)}{b} \]
Antiderivative was successfully verified.
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Rule 8
Rule 3767
Rubi steps
\begin {align*} \int \csc ^2(a+b x) \, dx &=-\frac {\operatorname {Subst}(\int 1 \, dx,x,\cot (a+b x))}{b}\\ &=-\frac {\cot (a+b x)}{b}\\ \end {align*}
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Mathematica [A] time = 0.01, size = 11, normalized size = 1.00 \[ -\frac {\cot (a+b x)}{b} \]
Antiderivative was successfully verified.
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fricas [A] time = 0.44, size = 19, normalized size = 1.73 \[ -\frac {\cos \left (b x + a\right )}{b \sin \left (b x + a\right )} \]
Verification of antiderivative is not currently implemented for this CAS.
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giac [A] time = 0.21, size = 13, normalized size = 1.18 \[ -\frac {1}{b \tan \left (b x + a\right )} \]
Verification of antiderivative is not currently implemented for this CAS.
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maple [A] time = 0.82, size = 12, normalized size = 1.09 \[ -\frac {\cot \left (b x +a \right )}{b} \]
Verification of antiderivative is not currently implemented for this CAS.
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maxima [A] time = 0.33, size = 13, normalized size = 1.18 \[ -\frac {1}{b \tan \left (b x + a\right )} \]
Verification of antiderivative is not currently implemented for this CAS.
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mupad [B] time = 0.10, size = 11, normalized size = 1.00 \[ -\frac {\mathrm {cot}\left (a+b\,x\right )}{b} \]
Verification of antiderivative is not currently implemented for this CAS.
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sympy [F] time = 0.00, size = 0, normalized size = 0.00 \[ \int \csc ^{2}{\left (a + b x \right )}\, dx \]
Verification of antiderivative is not currently implemented for this CAS.
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