Optimal. Leaf size=86 \[ -\frac {a^7}{x}+21 a^5 b^2 x+\frac {35}{2} a^4 b^3 x^2+\frac {35}{3} a^3 b^4 x^3+\frac {21}{4} a^2 b^5 x^4+\frac {7}{5} a b^6 x^5+\frac {b^7 x^6}{6}+7 a^6 b \log (x) \]
[Out]
________________________________________________________________________________________
Rubi [A]
time = 0.02, antiderivative size = 86, normalized size of antiderivative = 1.00, number of steps
used = 2, number of rules used = 1, integrand size = 11, \(\frac {\text {number of rules}}{\text {integrand size}}\) = 0.091, Rules used = {45}
\begin {gather*} -\frac {a^7}{x}+7 a^6 b \log (x)+21 a^5 b^2 x+\frac {35}{2} a^4 b^3 x^2+\frac {35}{3} a^3 b^4 x^3+\frac {21}{4} a^2 b^5 x^4+\frac {7}{5} a b^6 x^5+\frac {b^7 x^6}{6} \end {gather*}
Antiderivative was successfully verified.
[In]
[Out]
Rule 45
Rubi steps
\begin {align*} \int \frac {(a+b x)^7}{x^2} \, dx &=\int \left (21 a^5 b^2+\frac {a^7}{x^2}+\frac {7 a^6 b}{x}+35 a^4 b^3 x+35 a^3 b^4 x^2+21 a^2 b^5 x^3+7 a b^6 x^4+b^7 x^5\right ) \, dx\\ &=-\frac {a^7}{x}+21 a^5 b^2 x+\frac {35}{2} a^4 b^3 x^2+\frac {35}{3} a^3 b^4 x^3+\frac {21}{4} a^2 b^5 x^4+\frac {7}{5} a b^6 x^5+\frac {b^7 x^6}{6}+7 a^6 b \log (x)\\ \end {align*}
________________________________________________________________________________________
Mathematica [A]
time = 0.00, size = 86, normalized size = 1.00 \begin {gather*} -\frac {a^7}{x}+21 a^5 b^2 x+\frac {35}{2} a^4 b^3 x^2+\frac {35}{3} a^3 b^4 x^3+\frac {21}{4} a^2 b^5 x^4+\frac {7}{5} a b^6 x^5+\frac {b^7 x^6}{6}+7 a^6 b \log (x) \end {gather*}
Antiderivative was successfully verified.
[In]
[Out]
________________________________________________________________________________________
Maple [A]
time = 0.08, size = 77, normalized size = 0.90
method | result | size |
default | \(-\frac {a^{7}}{x}+21 a^{5} b^{2} x +\frac {35 a^{4} b^{3} x^{2}}{2}+\frac {35 a^{3} b^{4} x^{3}}{3}+\frac {21 a^{2} b^{5} x^{4}}{4}+\frac {7 a \,b^{6} x^{5}}{5}+\frac {b^{7} x^{6}}{6}+7 a^{6} b \ln \left (x \right )\) | \(77\) |
risch | \(-\frac {a^{7}}{x}+21 a^{5} b^{2} x +\frac {35 a^{4} b^{3} x^{2}}{2}+\frac {35 a^{3} b^{4} x^{3}}{3}+\frac {21 a^{2} b^{5} x^{4}}{4}+\frac {7 a \,b^{6} x^{5}}{5}+\frac {b^{7} x^{6}}{6}+7 a^{6} b \ln \left (x \right )\) | \(77\) |
norman | \(\frac {-a^{7}+\frac {1}{6} b^{7} x^{7}+\frac {7}{5} a \,b^{6} x^{6}+\frac {21}{4} a^{2} b^{5} x^{5}+\frac {35}{3} a^{3} b^{4} x^{4}+\frac {35}{2} a^{4} b^{3} x^{3}+21 a^{5} b^{2} x^{2}}{x}+7 a^{6} b \ln \left (x \right )\) | \(81\) |
Verification of antiderivative is not currently implemented for this CAS.
[In]
[Out]
________________________________________________________________________________________
Maxima [A]
time = 0.28, size = 76, normalized size = 0.88 \begin {gather*} \frac {1}{6} \, b^{7} x^{6} + \frac {7}{5} \, a b^{6} x^{5} + \frac {21}{4} \, a^{2} b^{5} x^{4} + \frac {35}{3} \, a^{3} b^{4} x^{3} + \frac {35}{2} \, a^{4} b^{3} x^{2} + 21 \, a^{5} b^{2} x + 7 \, a^{6} b \log \left (x\right ) - \frac {a^{7}}{x} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
[In]
[Out]
________________________________________________________________________________________
Fricas [A]
time = 0.79, size = 81, normalized size = 0.94 \begin {gather*} \frac {10 \, b^{7} x^{7} + 84 \, a b^{6} x^{6} + 315 \, a^{2} b^{5} x^{5} + 700 \, a^{3} b^{4} x^{4} + 1050 \, a^{4} b^{3} x^{3} + 1260 \, a^{5} b^{2} x^{2} + 420 \, a^{6} b x \log \left (x\right ) - 60 \, a^{7}}{60 \, x} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
[In]
[Out]
________________________________________________________________________________________
Sympy [A]
time = 0.05, size = 85, normalized size = 0.99 \begin {gather*} - \frac {a^{7}}{x} + 7 a^{6} b \log {\left (x \right )} + 21 a^{5} b^{2} x + \frac {35 a^{4} b^{3} x^{2}}{2} + \frac {35 a^{3} b^{4} x^{3}}{3} + \frac {21 a^{2} b^{5} x^{4}}{4} + \frac {7 a b^{6} x^{5}}{5} + \frac {b^{7} x^{6}}{6} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
[In]
[Out]
________________________________________________________________________________________
Giac [A]
time = 1.32, size = 77, normalized size = 0.90 \begin {gather*} \frac {1}{6} \, b^{7} x^{6} + \frac {7}{5} \, a b^{6} x^{5} + \frac {21}{4} \, a^{2} b^{5} x^{4} + \frac {35}{3} \, a^{3} b^{4} x^{3} + \frac {35}{2} \, a^{4} b^{3} x^{2} + 21 \, a^{5} b^{2} x + 7 \, a^{6} b \log \left ({\left | x \right |}\right ) - \frac {a^{7}}{x} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
[In]
[Out]
________________________________________________________________________________________
Mupad [B]
time = 0.05, size = 76, normalized size = 0.88 \begin {gather*} \frac {b^7\,x^6}{6}-\frac {a^7}{x}+21\,a^5\,b^2\,x+\frac {7\,a\,b^6\,x^5}{5}+7\,a^6\,b\,\ln \left (x\right )+\frac {35\,a^4\,b^3\,x^2}{2}+\frac {35\,a^3\,b^4\,x^3}{3}+\frac {21\,a^2\,b^5\,x^4}{4} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
[In]
[Out]
________________________________________________________________________________________