Integrand size = 31, antiderivative size = 201 \[ \int \tan ^2(c+d x) (a+b \tan (c+d x))^3 (A+B \tan (c+d x)) \, dx=-\left (\left (a^3 A-3 a A b^2-3 a^2 b B+b^3 B\right ) x\right )+\frac {\left (3 a^2 A b-A b^3+a^3 B-3 a b^2 B\right ) \log (\cos (c+d x))}{d}-\frac {b \left (2 a A b+a^2 B-b^2 B\right ) \tan (c+d x)}{d}-\frac {(A b+a B) (a+b \tan (c+d x))^2}{2 d}-\frac {B (a+b \tan (c+d x))^3}{3 d}+\frac {(5 A b-a B) (a+b \tan (c+d x))^4}{20 b^2 d}+\frac {B \tan (c+d x) (a+b \tan (c+d x))^4}{5 b d} \]
[Out]
Time = 0.61 (sec) , antiderivative size = 201, normalized size of antiderivative = 1.00, number of steps used = 6, number of rules used = 5, \(\frac {\text {number of rules}}{\text {integrand size}}\) = 0.161, Rules used = {3688, 3711, 3609, 3606, 3556} \[ \int \tan ^2(c+d x) (a+b \tan (c+d x))^3 (A+B \tan (c+d x)) \, dx=-\frac {b \left (a^2 B+2 a A b-b^2 B\right ) \tan (c+d x)}{d}+\frac {\left (a^3 B+3 a^2 A b-3 a b^2 B-A b^3\right ) \log (\cos (c+d x))}{d}-x \left (a^3 A-3 a^2 b B-3 a A b^2+b^3 B\right )+\frac {(5 A b-a B) (a+b \tan (c+d x))^4}{20 b^2 d}-\frac {(a B+A b) (a+b \tan (c+d x))^2}{2 d}+\frac {B \tan (c+d x) (a+b \tan (c+d x))^4}{5 b d}-\frac {B (a+b \tan (c+d x))^3}{3 d} \]
[In]
[Out]
Rule 3556
Rule 3606
Rule 3609
Rule 3688
Rule 3711
Rubi steps \begin{align*} \text {integral}& = \frac {B \tan (c+d x) (a+b \tan (c+d x))^4}{5 b d}+\frac {\int (a+b \tan (c+d x))^3 \left (-a B-5 b B \tan (c+d x)+(5 A b-a B) \tan ^2(c+d x)\right ) \, dx}{5 b} \\ & = \frac {(5 A b-a B) (a+b \tan (c+d x))^4}{20 b^2 d}+\frac {B \tan (c+d x) (a+b \tan (c+d x))^4}{5 b d}+\frac {\int (a+b \tan (c+d x))^3 (-5 A b-5 b B \tan (c+d x)) \, dx}{5 b} \\ & = -\frac {B (a+b \tan (c+d x))^3}{3 d}+\frac {(5 A b-a B) (a+b \tan (c+d x))^4}{20 b^2 d}+\frac {B \tan (c+d x) (a+b \tan (c+d x))^4}{5 b d}+\frac {\int (a+b \tan (c+d x))^2 (-5 b (a A-b B)-5 b (A b+a B) \tan (c+d x)) \, dx}{5 b} \\ & = -\frac {(A b+a B) (a+b \tan (c+d x))^2}{2 d}-\frac {B (a+b \tan (c+d x))^3}{3 d}+\frac {(5 A b-a B) (a+b \tan (c+d x))^4}{20 b^2 d}+\frac {B \tan (c+d x) (a+b \tan (c+d x))^4}{5 b d}+\frac {\int (a+b \tan (c+d x)) \left (-5 b \left (a^2 A-A b^2-2 a b B\right )-5 b \left (2 a A b+a^2 B-b^2 B\right ) \tan (c+d x)\right ) \, dx}{5 b} \\ & = -\left (\left (a^3 A-3 a A b^2-3 a^2 b B+b^3 B\right ) x\right )-\frac {b \left (2 a A b+a^2 B-b^2 B\right ) \tan (c+d x)}{d}-\frac {(A b+a B) (a+b \tan (c+d x))^2}{2 d}-\frac {B (a+b \tan (c+d x))^3}{3 d}+\frac {(5 A b-a B) (a+b \tan (c+d x))^4}{20 b^2 d}+\frac {B \tan (c+d x) (a+b \tan (c+d x))^4}{5 b d}+\left (-3 a^2 A b+A b^3-a^3 B+3 a b^2 B\right ) \int \tan (c+d x) \, dx \\ & = -\left (\left (a^3 A-3 a A b^2-3 a^2 b B+b^3 B\right ) x\right )+\frac {\left (3 a^2 A b-A b^3+a^3 B-3 a b^2 B\right ) \log (\cos (c+d x))}{d}-\frac {b \left (2 a A b+a^2 B-b^2 B\right ) \tan (c+d x)}{d}-\frac {(A b+a B) (a+b \tan (c+d x))^2}{2 d}-\frac {B (a+b \tan (c+d x))^3}{3 d}+\frac {(5 A b-a B) (a+b \tan (c+d x))^4}{20 b^2 d}+\frac {B \tan (c+d x) (a+b \tan (c+d x))^4}{5 b d} \\ \end{align*}
Result contains complex when optimal does not.
Time = 2.37 (sec) , antiderivative size = 241, normalized size of antiderivative = 1.20 \[ \int \tan ^2(c+d x) (a+b \tan (c+d x))^3 (A+B \tan (c+d x)) \, dx=\frac {\frac {3 (5 A b-a B) (a+b \tan (c+d x))^4}{b}+12 B \tan (c+d x) (a+b \tan (c+d x))^4-30 (A b-a B) \left ((i a-b)^3 \log (i-\tan (c+d x))-(i a+b)^3 \log (i+\tan (c+d x))+6 a b^2 \tan (c+d x)+b^3 \tan ^2(c+d x)\right )+10 B \left (3 i (a+i b)^4 \log (i-\tan (c+d x))-3 i (a-i b)^4 \log (i+\tan (c+d x))+6 b^2 \left (-6 a^2+b^2\right ) \tan (c+d x)-12 a b^3 \tan ^2(c+d x)-2 b^4 \tan ^3(c+d x)\right )}{60 b d} \]
[In]
[Out]
Time = 0.10 (sec) , antiderivative size = 207, normalized size of antiderivative = 1.03
method | result | size |
parts | \(\frac {\left (A \,b^{3}+3 B a \,b^{2}\right ) \left (\frac {\left (\tan ^{4}\left (d x +c \right )\right )}{4}-\frac {\left (\tan ^{2}\left (d x +c \right )\right )}{2}+\frac {\ln \left (1+\tan ^{2}\left (d x +c \right )\right )}{2}\right )}{d}+\frac {\left (3 A a \,b^{2}+3 B \,a^{2} b \right ) \left (\frac {\left (\tan ^{3}\left (d x +c \right )\right )}{3}-\tan \left (d x +c \right )+\arctan \left (\tan \left (d x +c \right )\right )\right )}{d}+\frac {\left (3 A \,a^{2} b +B \,a^{3}\right ) \left (\frac {\left (\tan ^{2}\left (d x +c \right )\right )}{2}-\frac {\ln \left (1+\tan ^{2}\left (d x +c \right )\right )}{2}\right )}{d}+\frac {A \,a^{3} \left (\tan \left (d x +c \right )-\arctan \left (\tan \left (d x +c \right )\right )\right )}{d}+\frac {B \,b^{3} \left (\frac {\left (\tan ^{5}\left (d x +c \right )\right )}{5}-\frac {\left (\tan ^{3}\left (d x +c \right )\right )}{3}+\tan \left (d x +c \right )-\arctan \left (\tan \left (d x +c \right )\right )\right )}{d}\) | \(207\) |
norman | \(\left (-A \,a^{3}+3 A a \,b^{2}+3 B \,a^{2} b -B \,b^{3}\right ) x +\frac {\left (A \,a^{3}-3 A a \,b^{2}-3 B \,a^{2} b +B \,b^{3}\right ) \tan \left (d x +c \right )}{d}+\frac {\left (3 A \,a^{2} b -A \,b^{3}+B \,a^{3}-3 B a \,b^{2}\right ) \left (\tan ^{2}\left (d x +c \right )\right )}{2 d}+\frac {B \,b^{3} \left (\tan ^{5}\left (d x +c \right )\right )}{5 d}+\frac {b \left (3 A a b +3 B \,a^{2}-B \,b^{2}\right ) \left (\tan ^{3}\left (d x +c \right )\right )}{3 d}+\frac {b^{2} \left (A b +3 B a \right ) \left (\tan ^{4}\left (d x +c \right )\right )}{4 d}-\frac {\left (3 A \,a^{2} b -A \,b^{3}+B \,a^{3}-3 B a \,b^{2}\right ) \ln \left (1+\tan ^{2}\left (d x +c \right )\right )}{2 d}\) | \(220\) |
derivativedivides | \(\frac {\frac {B \,b^{3} \left (\tan ^{5}\left (d x +c \right )\right )}{5}+\frac {A \,b^{3} \left (\tan ^{4}\left (d x +c \right )\right )}{4}+\frac {3 B a \,b^{2} \left (\tan ^{4}\left (d x +c \right )\right )}{4}+A a \,b^{2} \left (\tan ^{3}\left (d x +c \right )\right )+B \,a^{2} b \left (\tan ^{3}\left (d x +c \right )\right )-\frac {B \,b^{3} \left (\tan ^{3}\left (d x +c \right )\right )}{3}+\frac {3 A \,a^{2} b \left (\tan ^{2}\left (d x +c \right )\right )}{2}-\frac {A \,b^{3} \left (\tan ^{2}\left (d x +c \right )\right )}{2}+\frac {B \left (\tan ^{2}\left (d x +c \right )\right ) a^{3}}{2}-\frac {3 B a \,b^{2} \left (\tan ^{2}\left (d x +c \right )\right )}{2}+A \tan \left (d x +c \right ) a^{3}-3 A a \,b^{2} \tan \left (d x +c \right )-3 B \,a^{2} b \tan \left (d x +c \right )+B \,b^{3} \tan \left (d x +c \right )+\frac {\left (-3 A \,a^{2} b +A \,b^{3}-B \,a^{3}+3 B a \,b^{2}\right ) \ln \left (1+\tan ^{2}\left (d x +c \right )\right )}{2}+\left (-A \,a^{3}+3 A a \,b^{2}+3 B \,a^{2} b -B \,b^{3}\right ) \arctan \left (\tan \left (d x +c \right )\right )}{d}\) | \(271\) |
default | \(\frac {\frac {B \,b^{3} \left (\tan ^{5}\left (d x +c \right )\right )}{5}+\frac {A \,b^{3} \left (\tan ^{4}\left (d x +c \right )\right )}{4}+\frac {3 B a \,b^{2} \left (\tan ^{4}\left (d x +c \right )\right )}{4}+A a \,b^{2} \left (\tan ^{3}\left (d x +c \right )\right )+B \,a^{2} b \left (\tan ^{3}\left (d x +c \right )\right )-\frac {B \,b^{3} \left (\tan ^{3}\left (d x +c \right )\right )}{3}+\frac {3 A \,a^{2} b \left (\tan ^{2}\left (d x +c \right )\right )}{2}-\frac {A \,b^{3} \left (\tan ^{2}\left (d x +c \right )\right )}{2}+\frac {B \left (\tan ^{2}\left (d x +c \right )\right ) a^{3}}{2}-\frac {3 B a \,b^{2} \left (\tan ^{2}\left (d x +c \right )\right )}{2}+A \tan \left (d x +c \right ) a^{3}-3 A a \,b^{2} \tan \left (d x +c \right )-3 B \,a^{2} b \tan \left (d x +c \right )+B \,b^{3} \tan \left (d x +c \right )+\frac {\left (-3 A \,a^{2} b +A \,b^{3}-B \,a^{3}+3 B a \,b^{2}\right ) \ln \left (1+\tan ^{2}\left (d x +c \right )\right )}{2}+\left (-A \,a^{3}+3 A a \,b^{2}+3 B \,a^{2} b -B \,b^{3}\right ) \arctan \left (\tan \left (d x +c \right )\right )}{d}\) | \(271\) |
parallelrisch | \(-\frac {-12 B \,b^{3} \left (\tan ^{5}\left (d x +c \right )\right )-15 A \,b^{3} \left (\tan ^{4}\left (d x +c \right )\right )-45 B a \,b^{2} \left (\tan ^{4}\left (d x +c \right )\right )-60 A a \,b^{2} \left (\tan ^{3}\left (d x +c \right )\right )-60 B \,a^{2} b \left (\tan ^{3}\left (d x +c \right )\right )+20 B \,b^{3} \left (\tan ^{3}\left (d x +c \right )\right )+60 A x \,a^{3} d -180 A a \,b^{2} d x -90 A \,a^{2} b \left (\tan ^{2}\left (d x +c \right )\right )+30 A \,b^{3} \left (\tan ^{2}\left (d x +c \right )\right )-180 B \,a^{2} b d x +60 B \,b^{3} d x -30 B \left (\tan ^{2}\left (d x +c \right )\right ) a^{3}+90 B a \,b^{2} \left (\tan ^{2}\left (d x +c \right )\right )+90 A \ln \left (1+\tan ^{2}\left (d x +c \right )\right ) a^{2} b -30 A \ln \left (1+\tan ^{2}\left (d x +c \right )\right ) b^{3}-60 A \tan \left (d x +c \right ) a^{3}+180 A a \,b^{2} \tan \left (d x +c \right )+30 B \ln \left (1+\tan ^{2}\left (d x +c \right )\right ) a^{3}-90 B \ln \left (1+\tan ^{2}\left (d x +c \right )\right ) a \,b^{2}+180 B \,a^{2} b \tan \left (d x +c \right )-60 B \,b^{3} \tan \left (d x +c \right )}{60 d}\) | \(306\) |
risch | \(-A \,a^{3} x +3 A a \,b^{2} x +3 B \,a^{2} b x -B \,b^{3} x +\frac {2 i A \,b^{3} c}{d}+\frac {6 i B a \,b^{2} c}{d}-3 i A \,a^{2} b x +i A \,b^{3} x -\frac {6 i A \,a^{2} b c}{d}-\frac {2 i a^{3} B c}{d}+\frac {2 i \left (-60 A a \,b^{2}-60 B \,a^{2} b +15 A \,a^{3}+23 B \,b^{3}-135 i A \,a^{2} b \,{\mathrm e}^{4 i \left (d x +c \right )}+180 i B a \,b^{2} {\mathrm e}^{4 i \left (d x +c \right )}-45 i A \,a^{2} b \,{\mathrm e}^{8 i \left (d x +c \right )}+90 i B a \,b^{2} {\mathrm e}^{8 i \left (d x +c \right )}+90 i B a \,b^{2} {\mathrm e}^{2 i \left (d x +c \right )}-45 i A \,a^{2} b \,{\mathrm e}^{2 i \left (d x +c \right )}-135 i A \,a^{2} b \,{\mathrm e}^{6 i \left (d x +c \right )}+180 i B a \,b^{2} {\mathrm e}^{6 i \left (d x +c \right )}+15 A \,a^{3} {\mathrm e}^{8 i \left (d x +c \right )}+45 B \,b^{3} {\mathrm e}^{8 i \left (d x +c \right )}+60 A \,a^{3} {\mathrm e}^{6 i \left (d x +c \right )}+90 B \,b^{3} {\mathrm e}^{6 i \left (d x +c \right )}+90 A \,a^{3} {\mathrm e}^{4 i \left (d x +c \right )}+140 B \,b^{3} {\mathrm e}^{4 i \left (d x +c \right )}+60 A \,a^{3} {\mathrm e}^{2 i \left (d x +c \right )}+70 B \,b^{3} {\mathrm e}^{2 i \left (d x +c \right )}+60 i A \,b^{3} {\mathrm e}^{4 i \left (d x +c \right )}-45 i B \,a^{3} {\mathrm e}^{4 i \left (d x +c \right )}+30 i A \,b^{3} {\mathrm e}^{2 i \left (d x +c \right )}+60 i A \,b^{3} {\mathrm e}^{6 i \left (d x +c \right )}-45 i B \,a^{3} {\mathrm e}^{6 i \left (d x +c \right )}-15 i B \,a^{3} {\mathrm e}^{2 i \left (d x +c \right )}-15 i B \,a^{3} {\mathrm e}^{8 i \left (d x +c \right )}+30 i A \,b^{3} {\mathrm e}^{8 i \left (d x +c \right )}-210 A a \,b^{2} {\mathrm e}^{2 i \left (d x +c \right )}-210 B \,a^{2} b \,{\mathrm e}^{2 i \left (d x +c \right )}-90 A a \,b^{2} {\mathrm e}^{8 i \left (d x +c \right )}-90 B \,a^{2} b \,{\mathrm e}^{8 i \left (d x +c \right )}-270 A a \,b^{2} {\mathrm e}^{6 i \left (d x +c \right )}-270 B \,a^{2} b \,{\mathrm e}^{6 i \left (d x +c \right )}-330 A a \,b^{2} {\mathrm e}^{4 i \left (d x +c \right )}-330 B \,a^{2} b \,{\mathrm e}^{4 i \left (d x +c \right )}\right )}{15 d \left ({\mathrm e}^{2 i \left (d x +c \right )}+1\right )^{5}}+3 i B a \,b^{2} x -i B \,a^{3} x +\frac {3 \ln \left ({\mathrm e}^{2 i \left (d x +c \right )}+1\right ) A \,a^{2} b}{d}-\frac {\ln \left ({\mathrm e}^{2 i \left (d x +c \right )}+1\right ) A \,b^{3}}{d}+\frac {a^{3} \ln \left ({\mathrm e}^{2 i \left (d x +c \right )}+1\right ) B}{d}-\frac {3 \ln \left ({\mathrm e}^{2 i \left (d x +c \right )}+1\right ) B a \,b^{2}}{d}\) | \(755\) |
[In]
[Out]
none
Time = 0.26 (sec) , antiderivative size = 213, normalized size of antiderivative = 1.06 \[ \int \tan ^2(c+d x) (a+b \tan (c+d x))^3 (A+B \tan (c+d x)) \, dx=\frac {12 \, B b^{3} \tan \left (d x + c\right )^{5} + 15 \, {\left (3 \, B a b^{2} + A b^{3}\right )} \tan \left (d x + c\right )^{4} + 20 \, {\left (3 \, B a^{2} b + 3 \, A a b^{2} - B b^{3}\right )} \tan \left (d x + c\right )^{3} - 60 \, {\left (A a^{3} - 3 \, B a^{2} b - 3 \, A a b^{2} + B b^{3}\right )} d x + 30 \, {\left (B a^{3} + 3 \, A a^{2} b - 3 \, B a b^{2} - A b^{3}\right )} \tan \left (d x + c\right )^{2} + 30 \, {\left (B a^{3} + 3 \, A a^{2} b - 3 \, B a b^{2} - A b^{3}\right )} \log \left (\frac {1}{\tan \left (d x + c\right )^{2} + 1}\right ) + 60 \, {\left (A a^{3} - 3 \, B a^{2} b - 3 \, A a b^{2} + B b^{3}\right )} \tan \left (d x + c\right )}{60 \, d} \]
[In]
[Out]
Leaf count of result is larger than twice the leaf count of optimal. 384 vs. \(2 (185) = 370\).
Time = 0.18 (sec) , antiderivative size = 384, normalized size of antiderivative = 1.91 \[ \int \tan ^2(c+d x) (a+b \tan (c+d x))^3 (A+B \tan (c+d x)) \, dx=\begin {cases} - A a^{3} x + \frac {A a^{3} \tan {\left (c + d x \right )}}{d} - \frac {3 A a^{2} b \log {\left (\tan ^{2}{\left (c + d x \right )} + 1 \right )}}{2 d} + \frac {3 A a^{2} b \tan ^{2}{\left (c + d x \right )}}{2 d} + 3 A a b^{2} x + \frac {A a b^{2} \tan ^{3}{\left (c + d x \right )}}{d} - \frac {3 A a b^{2} \tan {\left (c + d x \right )}}{d} + \frac {A b^{3} \log {\left (\tan ^{2}{\left (c + d x \right )} + 1 \right )}}{2 d} + \frac {A b^{3} \tan ^{4}{\left (c + d x \right )}}{4 d} - \frac {A b^{3} \tan ^{2}{\left (c + d x \right )}}{2 d} - \frac {B a^{3} \log {\left (\tan ^{2}{\left (c + d x \right )} + 1 \right )}}{2 d} + \frac {B a^{3} \tan ^{2}{\left (c + d x \right )}}{2 d} + 3 B a^{2} b x + \frac {B a^{2} b \tan ^{3}{\left (c + d x \right )}}{d} - \frac {3 B a^{2} b \tan {\left (c + d x \right )}}{d} + \frac {3 B a b^{2} \log {\left (\tan ^{2}{\left (c + d x \right )} + 1 \right )}}{2 d} + \frac {3 B a b^{2} \tan ^{4}{\left (c + d x \right )}}{4 d} - \frac {3 B a b^{2} \tan ^{2}{\left (c + d x \right )}}{2 d} - B b^{3} x + \frac {B b^{3} \tan ^{5}{\left (c + d x \right )}}{5 d} - \frac {B b^{3} \tan ^{3}{\left (c + d x \right )}}{3 d} + \frac {B b^{3} \tan {\left (c + d x \right )}}{d} & \text {for}\: d \neq 0 \\x \left (A + B \tan {\left (c \right )}\right ) \left (a + b \tan {\left (c \right )}\right )^{3} \tan ^{2}{\left (c \right )} & \text {otherwise} \end {cases} \]
[In]
[Out]
none
Time = 0.32 (sec) , antiderivative size = 214, normalized size of antiderivative = 1.06 \[ \int \tan ^2(c+d x) (a+b \tan (c+d x))^3 (A+B \tan (c+d x)) \, dx=\frac {12 \, B b^{3} \tan \left (d x + c\right )^{5} + 15 \, {\left (3 \, B a b^{2} + A b^{3}\right )} \tan \left (d x + c\right )^{4} + 20 \, {\left (3 \, B a^{2} b + 3 \, A a b^{2} - B b^{3}\right )} \tan \left (d x + c\right )^{3} + 30 \, {\left (B a^{3} + 3 \, A a^{2} b - 3 \, B a b^{2} - A b^{3}\right )} \tan \left (d x + c\right )^{2} - 60 \, {\left (A a^{3} - 3 \, B a^{2} b - 3 \, A a b^{2} + B b^{3}\right )} {\left (d x + c\right )} - 30 \, {\left (B a^{3} + 3 \, A a^{2} b - 3 \, B a b^{2} - A b^{3}\right )} \log \left (\tan \left (d x + c\right )^{2} + 1\right ) + 60 \, {\left (A a^{3} - 3 \, B a^{2} b - 3 \, A a b^{2} + B b^{3}\right )} \tan \left (d x + c\right )}{60 \, d} \]
[In]
[Out]
Leaf count of result is larger than twice the leaf count of optimal. 3757 vs. \(2 (192) = 384\).
Time = 3.79 (sec) , antiderivative size = 3757, normalized size of antiderivative = 18.69 \[ \int \tan ^2(c+d x) (a+b \tan (c+d x))^3 (A+B \tan (c+d x)) \, dx=\text {Too large to display} \]
[In]
[Out]
Time = 7.31 (sec) , antiderivative size = 217, normalized size of antiderivative = 1.08 \[ \int \tan ^2(c+d x) (a+b \tan (c+d x))^3 (A+B \tan (c+d x)) \, dx=\frac {\mathrm {tan}\left (c+d\,x\right )\,\left (A\,a^3+B\,b^3-3\,a\,b\,\left (A\,b+B\,a\right )\right )}{d}-\frac {{\mathrm {tan}\left (c+d\,x\right )}^3\,\left (\frac {B\,b^3}{3}-a\,b\,\left (A\,b+B\,a\right )\right )}{d}-x\,\left (A\,a^3-3\,B\,a^2\,b-3\,A\,a\,b^2+B\,b^3\right )+\frac {\ln \left ({\mathrm {tan}\left (c+d\,x\right )}^2+1\right )\,\left (-\frac {B\,a^3}{2}-\frac {3\,A\,a^2\,b}{2}+\frac {3\,B\,a\,b^2}{2}+\frac {A\,b^3}{2}\right )}{d}+\frac {{\mathrm {tan}\left (c+d\,x\right )}^4\,\left (\frac {A\,b^3}{4}+\frac {3\,B\,a\,b^2}{4}\right )}{d}-\frac {{\mathrm {tan}\left (c+d\,x\right )}^2\,\left (-\frac {B\,a^3}{2}-\frac {3\,A\,a^2\,b}{2}+\frac {3\,B\,a\,b^2}{2}+\frac {A\,b^3}{2}\right )}{d}+\frac {B\,b^3\,{\mathrm {tan}\left (c+d\,x\right )}^5}{5\,d} \]
[In]
[Out]