Integrand size = 14, antiderivative size = 19 \[ \int \frac {-15-24 x^6}{32 x^6} \, dx=-2+5 e^4+\frac {3}{32 x^5}-\frac {3 x}{4} \]
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Time = 0.00 (sec) , antiderivative size = 13, normalized size of antiderivative = 0.68, number of steps used = 3, number of rules used = 2, \(\frac {\text {number of rules}}{\text {integrand size}}\) = 0.143, Rules used = {12, 14} \[ \int \frac {-15-24 x^6}{32 x^6} \, dx=\frac {3}{32 x^5}-\frac {3 x}{4} \]
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Rule 12
Rule 14
Rubi steps \begin{align*} \text {integral}& = \frac {1}{32} \int \frac {-15-24 x^6}{x^6} \, dx \\ & = \frac {1}{32} \int \left (-24-\frac {15}{x^6}\right ) \, dx \\ & = \frac {3}{32 x^5}-\frac {3 x}{4} \\ \end{align*}
Time = 0.00 (sec) , antiderivative size = 11, normalized size of antiderivative = 0.58 \[ \int \frac {-15-24 x^6}{32 x^6} \, dx=\frac {3}{32} \left (\frac {1}{x^5}-8 x\right ) \]
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Time = 0.02 (sec) , antiderivative size = 10, normalized size of antiderivative = 0.53
method | result | size |
default | \(-\frac {3 x}{4}+\frac {3}{32 x^{5}}\) | \(10\) |
risch | \(-\frac {3 x}{4}+\frac {3}{32 x^{5}}\) | \(10\) |
norman | \(\frac {\frac {3}{32}-\frac {3 x^{6}}{4}}{x^{5}}\) | \(12\) |
gosper | \(-\frac {3 \left (8 x^{6}-1\right )}{32 x^{5}}\) | \(13\) |
parallelrisch | \(-\frac {24 x^{6}-3}{32 x^{5}}\) | \(13\) |
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Time = 0.23 (sec) , antiderivative size = 12, normalized size of antiderivative = 0.63 \[ \int \frac {-15-24 x^6}{32 x^6} \, dx=-\frac {3 \, {\left (8 \, x^{6} - 1\right )}}{32 \, x^{5}} \]
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Time = 0.04 (sec) , antiderivative size = 10, normalized size of antiderivative = 0.53 \[ \int \frac {-15-24 x^6}{32 x^6} \, dx=- \frac {3 x}{4} + \frac {3}{32 x^{5}} \]
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none
Time = 0.17 (sec) , antiderivative size = 9, normalized size of antiderivative = 0.47 \[ \int \frac {-15-24 x^6}{32 x^6} \, dx=-\frac {3}{4} \, x + \frac {3}{32 \, x^{5}} \]
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Time = 0.29 (sec) , antiderivative size = 9, normalized size of antiderivative = 0.47 \[ \int \frac {-15-24 x^6}{32 x^6} \, dx=-\frac {3}{4} \, x + \frac {3}{32 \, x^{5}} \]
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Time = 0.03 (sec) , antiderivative size = 9, normalized size of antiderivative = 0.47 \[ \int \frac {-15-24 x^6}{32 x^6} \, dx=\frac {3}{32\,x^5}-\frac {3\,x}{4} \]
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