\(\int (c+d x)^m \tan ^3(a+b x) \, dx\) [303]

Optimal result

Integrand size = 16, antiderivative size = 16 \[ \int (c+d x)^m \tan ^3(a+b x) \, dx=\text {Int}\left ((c+d x)^m \tan ^3(a+b x),x\right ) \]

[Out]

Unintegrable((d*x+c)^m*tan(b*x+a)^3,x)

Rubi [N/A]

Not integrable

Time = 0.04 (sec) , antiderivative size = 16, 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 = {} \[ \int (c+d x)^m \tan ^3(a+b x) \, dx=\int (c+d x)^m \tan ^3(a+b x) \, dx \]

[In]

Int[(c + d*x)^m*Tan[a + b*x]^3,x]

[Out]

Defer[Int][(c + d*x)^m*Tan[a + b*x]^3, x]

Rubi steps \begin{align*} \text {integral}& = \int (c+d x)^m \tan ^3(a+b x) \, dx \\ \end{align*}

Mathematica [N/A]

Not integrable

Time = 10.90 (sec) , antiderivative size = 18, normalized size of antiderivative = 1.12 \[ \int (c+d x)^m \tan ^3(a+b x) \, dx=\int (c+d x)^m \tan ^3(a+b x) \, dx \]

[In]

Integrate[(c + d*x)^m*Tan[a + b*x]^3,x]

[Out]

Integrate[(c + d*x)^m*Tan[a + b*x]^3, x]

Maple [N/A] (verified)

Not integrable

Time = 0.19 (sec) , antiderivative size = 16, normalized size of antiderivative = 1.00

\[\int \left (d x +c \right )^{m} \tan \left (x b +a \right )^{3}d x\]

[In]

int((d*x+c)^m*tan(b*x+a)^3,x)

[Out]

int((d*x+c)^m*tan(b*x+a)^3,x)

Fricas [N/A]

Not integrable

Time = 0.24 (sec) , antiderivative size = 18, normalized size of antiderivative = 1.12 \[ \int (c+d x)^m \tan ^3(a+b x) \, dx=\int { {\left (d x + c\right )}^{m} \tan \left (b x + a\right )^{3} \,d x } \]

[In]

integrate((d*x+c)^m*tan(b*x+a)^3,x, algorithm="fricas")

[Out]

integral((d*x + c)^m*tan(b*x + a)^3, x)

Sympy [N/A]

Not integrable

Time = 1.56 (sec) , antiderivative size = 15, normalized size of antiderivative = 0.94 \[ \int (c+d x)^m \tan ^3(a+b x) \, dx=\int \left (c + d x\right )^{m} \tan ^{3}{\left (a + b x \right )}\, dx \]

[In]

integrate((d*x+c)**m*tan(b*x+a)**3,x)

[Out]

Integral((c + d*x)**m*tan(a + b*x)**3, x)

Maxima [N/A]

Not integrable

Time = 0.76 (sec) , antiderivative size = 18, normalized size of antiderivative = 1.12 \[ \int (c+d x)^m \tan ^3(a+b x) \, dx=\int { {\left (d x + c\right )}^{m} \tan \left (b x + a\right )^{3} \,d x } \]

[In]

integrate((d*x+c)^m*tan(b*x+a)^3,x, algorithm="maxima")

[Out]

integrate((d*x + c)^m*tan(b*x + a)^3, x)

Giac [N/A]

Not integrable

Time = 0.85 (sec) , antiderivative size = 18, normalized size of antiderivative = 1.12 \[ \int (c+d x)^m \tan ^3(a+b x) \, dx=\int { {\left (d x + c\right )}^{m} \tan \left (b x + a\right )^{3} \,d x } \]

[In]

integrate((d*x+c)^m*tan(b*x+a)^3,x, algorithm="giac")

[Out]

integrate((d*x + c)^m*tan(b*x + a)^3, x)

Mupad [N/A]

Not integrable

Time = 25.34 (sec) , antiderivative size = 18, normalized size of antiderivative = 1.12 \[ \int (c+d x)^m \tan ^3(a+b x) \, dx=\int {\mathrm {tan}\left (a+b\,x\right )}^3\,{\left (c+d\,x\right )}^m \,d x \]

[In]

int(tan(a + b*x)^3*(c + d*x)^m,x)

[Out]

int(tan(a + b*x)^3*(c + d*x)^m, x)