\(\int (10-18 x-45 x^2-12 x^3+15 x^4+3 \log (\frac {5}{4})) \, dx\) [3241]

Optimal result

Integrand size = 26, antiderivative size = 26 \[ \int \left (10-18 x-45 x^2-12 x^3+15 x^4+3 \log \left (\frac {5}{4}\right )\right ) \, dx=x+3 (3-x) \left (-3-\left (x+x^2\right )^2-\log \left (\frac {5}{4}\right )\right ) \]

[Out]

x+3*(-(x^2+x)^2+ln(4/5)-3)*(-x+3)

Rubi [A] (verified)

Time = 0.00 (sec) , antiderivative size = 31, normalized size of antiderivative = 1.19, number of steps used = 1, number of rules used = 0, \(\frac {\text {number of rules}}{\text {integrand size}}\) = 0.000, Rules used = {} \[ \int \left (10-18 x-45 x^2-12 x^3+15 x^4+3 \log \left (\frac {5}{4}\right )\right ) \, dx=3 x^5-3 x^4-15 x^3-9 x^2+x \left (10+3 \log \left (\frac {5}{4}\right )\right ) \]

[In]

Int[10 - 18*x - 45*x^2 - 12*x^3 + 15*x^4 + 3*Log[5/4],x]

[Out]

-9*x^2 - 15*x^3 - 3*x^4 + 3*x^5 + x*(10 + 3*Log[5/4])

Rubi steps \begin{align*} \text {integral}& = -9 x^2-15 x^3-3 x^4+3 x^5+x \left (10+3 \log \left (\frac {5}{4}\right )\right ) \\ \end{align*}

Mathematica [A] (verified)

Time = 0.00 (sec) , antiderivative size = 31, normalized size of antiderivative = 1.19 \[ \int \left (10-18 x-45 x^2-12 x^3+15 x^4+3 \log \left (\frac {5}{4}\right )\right ) \, dx=10 x-9 x^2-15 x^3-3 x^4+3 x^5+3 x \log \left (\frac {5}{4}\right ) \]

[In]

Integrate[10 - 18*x - 45*x^2 - 12*x^3 + 15*x^4 + 3*Log[5/4],x]

[Out]

10*x - 9*x^2 - 15*x^3 - 3*x^4 + 3*x^5 + 3*x*Log[5/4]

Maple [A] (verified)

Time = 0.30 (sec) , antiderivative size = 28, normalized size of antiderivative = 1.08

method	result	size
gosper	\(-x \left (-3 x^{4}+3 x^{3}+15 x^{2}+3 \ln \left (\frac {4}{5}\right )+9 x -10\right )\)	\(28\)
default	\(-3 x \ln \left (\frac {4}{5}\right )+3 x^{5}-3 x^{4}-15 x^{3}-9 x^{2}+10 x\)	\(30\)
parallelrisch	\(3 x^{5}-3 x^{4}-15 x^{3}-9 x^{2}+\left (-3 \ln \left (\frac {4}{5}\right )+10\right ) x\)	\(30\)
parts	\(-3 x \ln \left (\frac {4}{5}\right )+3 x^{5}-3 x^{4}-15 x^{3}-9 x^{2}+10 x\)	\(30\)
norman	\(\left (3 \ln \left (5\right )-6 \ln \left (2\right )+10\right ) x -9 x^{2}-15 x^{3}-3 x^{4}+3 x^{5}\)	\(34\)
risch	\(3 x^{5}-3 x^{4}-15 x^{3}-6 x \ln \left (2\right )+3 x \ln \left (5\right )-9 x^{2}+10 x\)	\(35\)

[In]

int(-3*ln(4/5)+15*x^4-12*x^3-45*x^2-18*x+10,x,method=_RETURNVERBOSE)

[Out]

-x*(-3*x^4+3*x^3+15*x^2+3*ln(4/5)+9*x-10)

Fricas [A] (verification not implemented)

none

Time = 0.23 (sec) , antiderivative size = 29, normalized size of antiderivative = 1.12 \[ \int \left (10-18 x-45 x^2-12 x^3+15 x^4+3 \log \left (\frac {5}{4}\right )\right ) \, dx=3 \, x^{5} - 3 \, x^{4} - 15 \, x^{3} - 9 \, x^{2} - 3 \, x \log \left (\frac {4}{5}\right ) + 10 \, x \]

[In]

integrate(-3*log(4/5)+15*x^4-12*x^3-45*x^2-18*x+10,x, algorithm="fricas")

[Out]

3*x^5 - 3*x^4 - 15*x^3 - 9*x^2 - 3*x*log(4/5) + 10*x

Sympy [A] (verification not implemented)

Time = 0.03 (sec) , antiderivative size = 32, normalized size of antiderivative = 1.23 \[ \int \left (10-18 x-45 x^2-12 x^3+15 x^4+3 \log \left (\frac {5}{4}\right )\right ) \, dx=3 x^{5} - 3 x^{4} - 15 x^{3} - 9 x^{2} + x \left (- 6 \log {\left (2 \right )} + 3 \log {\left (5 \right )} + 10\right ) \]

[In]

integrate(-3*ln(4/5)+15*x**4-12*x**3-45*x**2-18*x+10,x)

[Out]

3*x**5 - 3*x**4 - 15*x**3 - 9*x**2 + x*(-6*log(2) + 3*log(5) + 10)

Maxima [A] (verification not implemented)

none

Time = 0.19 (sec) , antiderivative size = 29, normalized size of antiderivative = 1.12 \[ \int \left (10-18 x-45 x^2-12 x^3+15 x^4+3 \log \left (\frac {5}{4}\right )\right ) \, dx=3 \, x^{5} - 3 \, x^{4} - 15 \, x^{3} - 9 \, x^{2} - 3 \, x \log \left (\frac {4}{5}\right ) + 10 \, x \]

[In]

integrate(-3*log(4/5)+15*x^4-12*x^3-45*x^2-18*x+10,x, algorithm="maxima")

[Out]

3*x^5 - 3*x^4 - 15*x^3 - 9*x^2 - 3*x*log(4/5) + 10*x

Giac [A] (verification not implemented)

none

Time = 0.25 (sec) , antiderivative size = 29, normalized size of antiderivative = 1.12 \[ \int \left (10-18 x-45 x^2-12 x^3+15 x^4+3 \log \left (\frac {5}{4}\right )\right ) \, dx=3 \, x^{5} - 3 \, x^{4} - 15 \, x^{3} - 9 \, x^{2} - 3 \, x \log \left (\frac {4}{5}\right ) + 10 \, x \]

[In]

integrate(-3*log(4/5)+15*x^4-12*x^3-45*x^2-18*x+10,x, algorithm="giac")

[Out]

3*x^5 - 3*x^4 - 15*x^3 - 9*x^2 - 3*x*log(4/5) + 10*x

Mupad [B] (verification not implemented)

Time = 0.03 (sec) , antiderivative size = 30, normalized size of antiderivative = 1.15 \[ \int \left (10-18 x-45 x^2-12 x^3+15 x^4+3 \log \left (\frac {5}{4}\right )\right ) \, dx=3\,x^5-3\,x^4-15\,x^3-9\,x^2+\left (10-3\,\ln \left (\frac {4}{5}\right )\right )\,x \]

[In]

int(15*x^4 - 3*log(4/5) - 45*x^2 - 12*x^3 - 18*x + 10,x)

[Out]

3*x^5 - 9*x^2 - 15*x^3 - 3*x^4 - x*(3*log(4/5) - 10)