Integrand size = 15, antiderivative size = 23 \[ \int \left (17+2 x-2 \log (x)-\log ^2(x)\right ) \, dx=-4+11 x+(3+x)^2+\frac {3}{\log (2)}-x \log ^2(x) \]
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Time = 0.01 (sec) , antiderivative size = 14, normalized size of antiderivative = 0.61, number of steps used = 4, number of rules used = 2, \(\frac {\text {number of rules}}{\text {integrand size}}\) = 0.133, Rules used = {2332, 2333} \[ \int \left (17+2 x-2 \log (x)-\log ^2(x)\right ) \, dx=x^2+17 x-x \log ^2(x) \]
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Rule 2332
Rule 2333
Rubi steps \begin{align*} \text {integral}& = 17 x+x^2-2 \int \log (x) \, dx-\int \log ^2(x) \, dx \\ & = 19 x+x^2-2 x \log (x)-x \log ^2(x)+2 \int \log (x) \, dx \\ & = 17 x+x^2-x \log ^2(x) \\ \end{align*}
Time = 0.00 (sec) , antiderivative size = 14, normalized size of antiderivative = 0.61 \[ \int \left (17+2 x-2 \log (x)-\log ^2(x)\right ) \, dx=17 x+x^2-x \log ^2(x) \]
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Time = 0.06 (sec) , antiderivative size = 15, normalized size of antiderivative = 0.65
method | result | size |
default | \(x^{2}+17 x -x \ln \left (x \right )^{2}\) | \(15\) |
norman | \(x^{2}+17 x -x \ln \left (x \right )^{2}\) | \(15\) |
risch | \(x^{2}+17 x -x \ln \left (x \right )^{2}\) | \(15\) |
parallelrisch | \(x^{2}+17 x -x \ln \left (x \right )^{2}\) | \(15\) |
parts | \(x^{2}+17 x -x \ln \left (x \right )^{2}\) | \(15\) |
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Time = 0.25 (sec) , antiderivative size = 14, normalized size of antiderivative = 0.61 \[ \int \left (17+2 x-2 \log (x)-\log ^2(x)\right ) \, dx=-x \log \left (x\right )^{2} + x^{2} + 17 \, x \]
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Time = 0.05 (sec) , antiderivative size = 12, normalized size of antiderivative = 0.52 \[ \int \left (17+2 x-2 \log (x)-\log ^2(x)\right ) \, dx=x^{2} - x \log {\left (x \right )}^{2} + 17 x \]
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Time = 0.20 (sec) , antiderivative size = 25, normalized size of antiderivative = 1.09 \[ \int \left (17+2 x-2 \log (x)-\log ^2(x)\right ) \, dx=-{\left (\log \left (x\right )^{2} - 2 \, \log \left (x\right ) + 2\right )} x + x^{2} - 2 \, x \log \left (x\right ) + 19 \, x \]
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Time = 0.27 (sec) , antiderivative size = 14, normalized size of antiderivative = 0.61 \[ \int \left (17+2 x-2 \log (x)-\log ^2(x)\right ) \, dx=-x \log \left (x\right )^{2} + x^{2} + 17 \, x \]
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Time = 11.40 (sec) , antiderivative size = 11, normalized size of antiderivative = 0.48 \[ \int \left (17+2 x-2 \log (x)-\log ^2(x)\right ) \, dx=x\,\left (-{\ln \left (x\right )}^2+x+17\right ) \]
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