3.100.93 \(\int \frac {-2+25 i \pi }{-1+25 i \pi } \, dx\)

Optimal. Leaf size=14 \[ -7+x+\frac {x}{1-25 i \pi } \]

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Rubi [A]  time = 0.00, antiderivative size = 18, normalized size of antiderivative = 1.29, number of steps used = 1, number of rules used = 1, integrand size = 17, \(\frac {\text {number of rules}}{\text {integrand size}}\) = 0.059, Rules used = {8} \begin {gather*} \frac {(25 \pi +2 i) x}{25 \pi +i} \end {gather*}

Antiderivative was successfully verified.

[In]

Int[(-2 + (25*I)*Pi)/(-1 + (25*I)*Pi),x]

[Out]

((2*I + 25*Pi)*x)/(I + 25*Pi)

Rule 8

Int[a_, x_Symbol] :> Simp[a*x, x] /; FreeQ[a, x]

Rubi steps

\begin {gather*} \begin {aligned} \text {integral} &=\frac {(2 i+25 \pi ) x}{i+25 \pi }\\ \end {aligned} \end {gather*}

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Mathematica [A]  time = 0.00, size = 28, normalized size = 2.00 \begin {gather*} -\frac {2 x}{-1+25 i \pi }+\frac {25 i \pi x}{-1+25 i \pi } \end {gather*}

Antiderivative was successfully verified.

[In]

Integrate[(-2 + (25*I)*Pi)/(-1 + (25*I)*Pi),x]

[Out]

(-2*x)/(-1 + (25*I)*Pi) + ((25*I)*Pi*x)/(-1 + (25*I)*Pi)

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fricas [A]  time = 1.91, size = 14, normalized size = 1.00 \begin {gather*} \frac {{\left (25 \, \pi + 2 i\right )} x}{25 \, \pi + i} \end {gather*}

Verification of antiderivative is not currently implemented for this CAS.

[In]

integrate((25*I*pi-2)/(25*I*pi-1),x, algorithm="fricas")

[Out]

(25*pi + 2*I)*x/(25*pi + I)

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giac [A]  time = 0.17, size = 14, normalized size = 1.00 \begin {gather*} \frac {{\left (25 i \, \pi - 2\right )} x}{25 i \, \pi - 1} \end {gather*}

Verification of antiderivative is not currently implemented for this CAS.

[In]

integrate((25*I*pi-2)/(25*I*pi-1),x, algorithm="giac")

[Out]

(25*I*pi - 2)*x/(25*I*pi - 1)

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maple [A]  time = 0.02, size = 17, normalized size = 1.21

method	result	size
default	\(\frac {\left (25 i \pi -2\right ) x}{25 i \pi -1}\)	\(17\)
norman	\(\frac {\left (625 \pi ^{2}+25 i \pi +2\right ) x}{625 \pi ^{2}+1}\)	\(23\)
risch	\(\frac {25 i x \pi }{25 i \pi -1}-\frac {2 x}{25 i \pi -1}\)	\(26\)

Verification of antiderivative is not currently implemented for this CAS.

[In]

int((25*I*Pi-2)/(25*I*Pi-1),x,method=_RETURNVERBOSE)

[Out]

(25*I*Pi-2)/(25*I*Pi-1)*x

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maxima [A]  time = 0.36, size = 14, normalized size = 1.00 \begin {gather*} \frac {{\left (25 i \, \pi - 2\right )} x}{25 i \, \pi - 1} \end {gather*}

Verification of antiderivative is not currently implemented for this CAS.

[In]

integrate((25*I*pi-2)/(25*I*pi-1),x, algorithm="maxima")

[Out]

(25*I*pi - 2)*x/(25*I*pi - 1)

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mupad [B]  time = 0.00, size = 16, normalized size = 1.14 \begin {gather*} \frac {x\,\left (-2+\Pi \,25{}\mathrm {i}\right )}{-1+\Pi \,25{}\mathrm {i}} \end {gather*}

Verification of antiderivative is not currently implemented for this CAS.

[In]

int((Pi*25i - 2)/(Pi*25i - 1),x)

[Out]

(x*(Pi*25i - 2))/(Pi*25i - 1)

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sympy [A]  time = 0.04, size = 14, normalized size = 1.00 \begin {gather*} \frac {x \left (-2 + 25 i \pi \right )}{-1 + 25 i \pi } \end {gather*}

Verification of antiderivative is not currently implemented for this CAS.

[In]

integrate((25*I*pi-2)/(25*I*pi-1),x)

[Out]

x*(-2 + 25*I*pi)/(-1 + 25*I*pi)

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