3.1442 \(\int \frac {x^6}{a+b x^7} \, dx\)

Optimal. Leaf size=15 \[ \frac {\log \left (a+b x^7\right )}{7 b} \]

[Out]

1/7*ln(b*x^7+a)/b

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Rubi [A]  time = 0.00, antiderivative size = 15, normalized size of antiderivative = 1.00, number of steps used = 1, number of rules used = 1, integrand size = 13, \(\frac {\text {number of rules}}{\text {integrand size}}\) = 0.077, Rules used = {260} \[ \frac {\log \left (a+b x^7\right )}{7 b} \]

Antiderivative was successfully verified.

[In]

Int[x^6/(a + b*x^7),x]

[Out]

Log[a + b*x^7]/(7*b)

Rule 260

Int[(x_)^(m_.)/((a_) + (b_.)*(x_)^(n_)), x_Symbol] :> Simp[Log[RemoveContent[a + b*x^n, x]]/(b*n), x] /; FreeQ
[{a, b, m, n}, x] && EqQ[m, n - 1]

Rubi steps

\begin {align*} \int \frac {x^6}{a+b x^7} \, dx &=\frac {\log \left (a+b x^7\right )}{7 b}\\ \end {align*}

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Mathematica [A]  time = 0.00, size = 15, normalized size = 1.00 \[ \frac {\log \left (a+b x^7\right )}{7 b} \]

Antiderivative was successfully verified.

[In]

Integrate[x^6/(a + b*x^7),x]

[Out]

Log[a + b*x^7]/(7*b)

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fricas [A]  time = 0.77, size = 13, normalized size = 0.87 \[ \frac {\log \left (b x^{7} + a\right )}{7 \, b} \]

Verification of antiderivative is not currently implemented for this CAS.

[In]

integrate(x^6/(b*x^7+a),x, algorithm="fricas")

[Out]

1/7*log(b*x^7 + a)/b

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giac [A]  time = 0.16, size = 14, normalized size = 0.93 \[ \frac {\log \left ({\left | b x^{7} + a \right |}\right )}{7 \, b} \]

Verification of antiderivative is not currently implemented for this CAS.

[In]

integrate(x^6/(b*x^7+a),x, algorithm="giac")

[Out]

1/7*log(abs(b*x^7 + a))/b

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maple [A]  time = 0.00, size = 14, normalized size = 0.93 \[ \frac {\ln \left (b \,x^{7}+a \right )}{7 b} \]

Verification of antiderivative is not currently implemented for this CAS.

[In]

int(x^6/(b*x^7+a),x)

[Out]

1/7*ln(b*x^7+a)/b

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maxima [A]  time = 1.01, size = 13, normalized size = 0.87 \[ \frac {\log \left (b x^{7} + a\right )}{7 \, b} \]

Verification of antiderivative is not currently implemented for this CAS.

[In]

integrate(x^6/(b*x^7+a),x, algorithm="maxima")

[Out]

1/7*log(b*x^7 + a)/b

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mupad [B]  time = 0.04, size = 13, normalized size = 0.87 \[ \frac {\ln \left (b\,x^7+a\right )}{7\,b} \]

Verification of antiderivative is not currently implemented for this CAS.

[In]

int(x^6/(a + b*x^7),x)

[Out]

log(a + b*x^7)/(7*b)

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sympy [A]  time = 0.33, size = 10, normalized size = 0.67 \[ \frac {\log {\left (a + b x^{7} \right )}}{7 b} \]

Verification of antiderivative is not currently implemented for this CAS.

[In]

integrate(x**6/(b*x**7+a),x)

[Out]

log(a + b*x**7)/(7*b)

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