\(\int \frac {(a+b x)^m (c+d x)^n (e+f x)^p}{g+h x} \, dx\) [143]

Optimal result

Integrand size = 29, antiderivative size = 29 \[ \int \frac {(a+b x)^m (c+d x)^n (e+f x)^p}{g+h x} \, dx=\text {Int}\left (\frac {(a+b x)^m (c+d x)^n (e+f x)^p}{g+h x},x\right ) \]

[Out]

CannotIntegrate((b*x+a)^m*(d*x+c)^n*(f*x+e)^p/(h*x+g),x)

Rubi [N/A]

Not integrable

Time = 0.00 (sec) , antiderivative size = 29, normalized size of antiderivative = 1.00, number of steps used = 0, number of rules used = 0, \(\frac {\text {number of rules}}{\text {integrand size}}\) = 0.000, Rules used = {} \[ \int \frac {(a+b x)^m (c+d x)^n (e+f x)^p}{g+h x} \, dx=\int \frac {(a+b x)^m (c+d x)^n (e+f x)^p}{g+h x} \, dx \]

[In]

Int[((a + b*x)^m*(c + d*x)^n*(e + f*x)^p)/(g + h*x),x]

[Out]

Defer[Int][((a + b*x)^m*(c + d*x)^n*(e + f*x)^p)/(g + h*x), x]

Rubi steps \begin{align*} \text {integral}& = \int \frac {(a+b x)^m (c+d x)^n (e+f x)^p}{g+h x} \, dx \\ \end{align*}

Mathematica [N/A]

Not integrable

Time = 0.75 (sec) , antiderivative size = 31, normalized size of antiderivative = 1.07 \[ \int \frac {(a+b x)^m (c+d x)^n (e+f x)^p}{g+h x} \, dx=\int \frac {(a+b x)^m (c+d x)^n (e+f x)^p}{g+h x} \, dx \]

[In]

Integrate[((a + b*x)^m*(c + d*x)^n*(e + f*x)^p)/(g + h*x),x]

[Out]

Integrate[((a + b*x)^m*(c + d*x)^n*(e + f*x)^p)/(g + h*x), x]

Maple [N/A]

Not integrable

Time = 0.12 (sec) , antiderivative size = 29, normalized size of antiderivative = 1.00

\[\int \frac {\left (b x +a \right )^{m} \left (d x +c \right )^{n} \left (f x +e \right )^{p}}{h x +g}d x\]

[In]

int((b*x+a)^m*(d*x+c)^n*(f*x+e)^p/(h*x+g),x)

[Out]

int((b*x+a)^m*(d*x+c)^n*(f*x+e)^p/(h*x+g),x)

Fricas [N/A]

Not integrable

Time = 0.27 (sec) , antiderivative size = 31, normalized size of antiderivative = 1.07 \[ \int \frac {(a+b x)^m (c+d x)^n (e+f x)^p}{g+h x} \, dx=\int { \frac {{\left (b x + a\right )}^{m} {\left (d x + c\right )}^{n} {\left (f x + e\right )}^{p}}{h x + g} \,d x } \]

[In]

integrate((b*x+a)^m*(d*x+c)^n*(f*x+e)^p/(h*x+g),x, algorithm="fricas")

[Out]

integral((b*x + a)^m*(d*x + c)^n*(f*x + e)^p/(h*x + g), x)

Sympy [F(-1)]

Timed out. \[ \int \frac {(a+b x)^m (c+d x)^n (e+f x)^p}{g+h x} \, dx=\text {Timed out} \]

[In]

integrate((b*x+a)**m*(d*x+c)**n*(f*x+e)**p/(h*x+g),x)

[Out]

Timed out

Maxima [N/A]

Not integrable

Time = 0.26 (sec) , antiderivative size = 31, normalized size of antiderivative = 1.07 \[ \int \frac {(a+b x)^m (c+d x)^n (e+f x)^p}{g+h x} \, dx=\int { \frac {{\left (b x + a\right )}^{m} {\left (d x + c\right )}^{n} {\left (f x + e\right )}^{p}}{h x + g} \,d x } \]

[In]

integrate((b*x+a)^m*(d*x+c)^n*(f*x+e)^p/(h*x+g),x, algorithm="maxima")

[Out]

integrate((b*x + a)^m*(d*x + c)^n*(f*x + e)^p/(h*x + g), x)

Giac [N/A]

Not integrable

Time = 0.28 (sec) , antiderivative size = 31, normalized size of antiderivative = 1.07 \[ \int \frac {(a+b x)^m (c+d x)^n (e+f x)^p}{g+h x} \, dx=\int { \frac {{\left (b x + a\right )}^{m} {\left (d x + c\right )}^{n} {\left (f x + e\right )}^{p}}{h x + g} \,d x } \]

[In]

integrate((b*x+a)^m*(d*x+c)^n*(f*x+e)^p/(h*x+g),x, algorithm="giac")

[Out]

integrate((b*x + a)^m*(d*x + c)^n*(f*x + e)^p/(h*x + g), x)

Mupad [N/A]

Not integrable

Time = 2.98 (sec) , antiderivative size = 31, normalized size of antiderivative = 1.07 \[ \int \frac {(a+b x)^m (c+d x)^n (e+f x)^p}{g+h x} \, dx=\int \frac {{\left (e+f\,x\right )}^p\,{\left (a+b\,x\right )}^m\,{\left (c+d\,x\right )}^n}{g+h\,x} \,d x \]

[In]

int(((e + f*x)^p*(a + b*x)^m*(c + d*x)^n)/(g + h*x),x)

[Out]

int(((e + f*x)^p*(a + b*x)^m*(c + d*x)^n)/(g + h*x), x)