\(\int (-9+10 x) \, dx\) [7515]

Optimal result

Integrand size = 5, antiderivative size = 16 \[ \int (-9+10 x) \, dx=x+5 \left (4-2 x+x^2+\log ^2(3)\right ) \]

[Out]

5*ln(3)^2+5*x^2+20-9*x

Rubi [A] (verified)

Time = 0.00 (sec) , antiderivative size = 9, normalized size of antiderivative = 0.56, number of steps used = 1, number of rules used = 0, \(\frac {\text {number of rules}}{\text {integrand size}}\) = 0.000, Rules used = {} \[ \int (-9+10 x) \, dx=5 x^2-9 x \]

[In]

Int[-9 + 10*x,x]

[Out]

-9*x + 5*x^2

Rubi steps \begin{align*} \text {integral}& = -9 x+5 x^2 \\ \end{align*}

Mathematica [A] (verified)

Time = 0.00 (sec) , antiderivative size = 9, normalized size of antiderivative = 0.56 \[ \int (-9+10 x) \, dx=-9 x+5 x^2 \]

[In]

Integrate[-9 + 10*x,x]

[Out]

-9*x + 5*x^2

Maple [A] (verified)

Time = 0.01 (sec) , antiderivative size = 10, normalized size of antiderivative = 0.62

method	result	size
gosper	\(5 x^{2}-9 x\)	\(10\)
default	\(5 x^{2}-9 x\)	\(10\)
norman	\(5 x^{2}-9 x\)	\(10\)
risch	\(5 x^{2}-9 x\)	\(10\)
parallelrisch	\(5 x^{2}-9 x\)	\(10\)
parts	\(5 x^{2}-9 x\)	\(10\)

[In]

int(10*x-9,x,method=_RETURNVERBOSE)

[Out]

5*x^2-9*x

Fricas [A] (verification not implemented)

none

Time = 0.23 (sec) , antiderivative size = 9, normalized size of antiderivative = 0.56 \[ \int (-9+10 x) \, dx=5 \, x^{2} - 9 \, x \]

[In]

integrate(10*x-9,x, algorithm="fricas")

[Out]

5*x^2 - 9*x

Sympy [A] (verification not implemented)

Time = 0.02 (sec) , antiderivative size = 7, normalized size of antiderivative = 0.44 \[ \int (-9+10 x) \, dx=5 x^{2} - 9 x \]

[In]

integrate(10*x-9,x)

[Out]

5*x**2 - 9*x

Maxima [A] (verification not implemented)

none

Time = 0.21 (sec) , antiderivative size = 9, normalized size of antiderivative = 0.56 \[ \int (-9+10 x) \, dx=5 \, x^{2} - 9 \, x \]

[In]

integrate(10*x-9,x, algorithm="maxima")

[Out]

5*x^2 - 9*x

Giac [A] (verification not implemented)

none

Time = 0.27 (sec) , antiderivative size = 9, normalized size of antiderivative = 0.56 \[ \int (-9+10 x) \, dx=5 \, x^{2} - 9 \, x \]

[In]

integrate(10*x-9,x, algorithm="giac")

[Out]

5*x^2 - 9*x

Mupad [B] (verification not implemented)

Time = 0.03 (sec) , antiderivative size = 7, normalized size of antiderivative = 0.44 \[ \int (-9+10 x) \, dx=x\,\left (5\,x-9\right ) \]

[In]

int(10*x - 9,x)

[Out]

x*(5*x - 9)