Integrand size = 20, antiderivative size = 20 \[ \int \frac {a x^2+b x^3+c x^4}{x^2} \, dx=a x+\frac {b x^2}{2}+\frac {c x^3}{3} \]
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Time = 0.00 (sec) , antiderivative size = 20, normalized size of antiderivative = 1.00, number of steps used = 2, number of rules used = 1, \(\frac {\text {number of rules}}{\text {integrand size}}\) = 0.050, Rules used = {14} \[ \int \frac {a x^2+b x^3+c x^4}{x^2} \, dx=a x+\frac {b x^2}{2}+\frac {c x^3}{3} \]
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Rule 14
Rubi steps \begin{align*} \text {integral}& = \int \left (a+b x+c x^2\right ) \, dx \\ & = a x+\frac {b x^2}{2}+\frac {c x^3}{3} \\ \end{align*}
Time = 0.01 (sec) , antiderivative size = 20, normalized size of antiderivative = 1.00 \[ \int \frac {a x^2+b x^3+c x^4}{x^2} \, dx=a x+\frac {b x^2}{2}+\frac {c x^3}{3} \]
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Time = 0.02 (sec) , antiderivative size = 17, normalized size of antiderivative = 0.85
method | result | size |
default | \(a x +\frac {1}{2} b \,x^{2}+\frac {1}{3} c \,x^{3}\) | \(17\) |
risch | \(a x +\frac {1}{2} b \,x^{2}+\frac {1}{3} c \,x^{3}\) | \(17\) |
parallelrisch | \(a x +\frac {1}{2} b \,x^{2}+\frac {1}{3} c \,x^{3}\) | \(17\) |
parts | \(a x +\frac {1}{2} b \,x^{2}+\frac {1}{3} c \,x^{3}\) | \(17\) |
gosper | \(\frac {x \left (2 c \,x^{2}+3 b x +6 a \right )}{6}\) | \(18\) |
norman | \(\frac {a \,x^{2}+\frac {1}{2} b \,x^{3}+\frac {1}{3} c \,x^{4}}{x}\) | \(23\) |
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none
Time = 0.24 (sec) , antiderivative size = 16, normalized size of antiderivative = 0.80 \[ \int \frac {a x^2+b x^3+c x^4}{x^2} \, dx=\frac {1}{3} \, c x^{3} + \frac {1}{2} \, b x^{2} + a x \]
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Time = 0.02 (sec) , antiderivative size = 15, normalized size of antiderivative = 0.75 \[ \int \frac {a x^2+b x^3+c x^4}{x^2} \, dx=a x + \frac {b x^{2}}{2} + \frac {c x^{3}}{3} \]
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none
Time = 0.19 (sec) , antiderivative size = 16, normalized size of antiderivative = 0.80 \[ \int \frac {a x^2+b x^3+c x^4}{x^2} \, dx=\frac {1}{3} \, c x^{3} + \frac {1}{2} \, b x^{2} + a x \]
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none
Time = 0.32 (sec) , antiderivative size = 16, normalized size of antiderivative = 0.80 \[ \int \frac {a x^2+b x^3+c x^4}{x^2} \, dx=\frac {1}{3} \, c x^{3} + \frac {1}{2} \, b x^{2} + a x \]
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Time = 0.01 (sec) , antiderivative size = 16, normalized size of antiderivative = 0.80 \[ \int \frac {a x^2+b x^3+c x^4}{x^2} \, dx=\frac {c\,x^3}{3}+\frac {b\,x^2}{2}+a\,x \]
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